21. Electronic Research Announcements Of The AMS surgery. Hutchings, Michael Michael Hutchings; Frank Morgan; ManuelRitor? Antonio Ros Proof of the double bubble conjecture. Kamber http://www.kurims.kyoto-u.ac.jp/EMIS/journals/ERA-AMS/era-auth-2000.html

This journal is archived by the American Mathematical Society. The master copy is available at http://www.ams.org/era/ 2000 Table of Contents - Indexed by Authors Adem, Alejandro Alejandro Adem; Jeff H. Smith On spaces with periodic cohomology Afraimovich, Valentin Valentin Afraimovich; Jean-René Chazottes; Benoît Saussol Local dimensions for Poincaré recurrences Bullett, S. R. S. R. Bullett; W. J. Harvey Mating quadratic maps with Kleinian groups via quasiconformal surgery Calegari, Danny Danny Calegari Chazottes, Jean-René Valentin Afraimovich; Jean-René Chazottes; Benoît Saussol Local dimensions for Poincaré recurrences Giambruno, A. A. Giambruno; M. Zaicev Minimal varieties of algebras of exponential growth Grishin, A. V. A. V. Grishin Harvey, W. J. S. R. Bullett; W. J. Harvey Mating quadratic maps with Kleinian groups via quasiconformal surgery Hutchings, Michael Michael Hutchings; Frank Morgan; Manuel Ritoré; Antonio Ros Proof of the double bubble conjecture Kamber, Franz W. Franz W. Kamber; Peter W. Michor The flow completion of a manifold with vector field Kirillov, A. A. A. A. Kirillov

22. Computer Images Of Double Bubbles By John Sullivan I created these images to illustrate the proof of the equalvolume caseof the double bubble conjecture by Hass and Schlafly in 1995. http://torus.math.uiuc.edu/jms/Images/double/

Standard and Nonstandard Double Bubbles John M Sullivan Click on any image for a larger (640x800) version. Please send me email ( jms@uiuc.edu ) for permission to publish these images, or to obtain even larger TIFF versions, with different background colors. These images show bubble clusters near equilibrium. The top row shows a standard double bubble of equal volumes, and a nonstandard cluster in which one bubble is a torus, forming a waist around the other. I created these images to illustrate the proof of the equal-volume case of the Double Bubble Conjecture by Hass and Schlafly in 1995. The bottom row shows a standard double bubble of unequal volumes (consisting of three spherical caps meeting at equal 120-degree angles), and a nonstandard bubble of the same volumes, in which the larger region is broken into two components (one a tiny ring around the other region). I created these images to illustrate the proof of the general Double Bubble Conjecture by Hutchings, Morgan, Ritore and Ros in 2000. In all four cases, the cluster is a surface of revolution. More details about the geometry of the examples with unequal volumes, including pictures of the generating curves, are available

23. Historia Matematica Mailing List Archive: [HM] Double Bubble Co HM double bubble conjecture Proved. Proof of the double bubble conjecture. by MichaelHutchings, Frank Morgan, Manuel Ritore, and Antonio Ros. quote History. http://sunsite.utk.edu/math_archives/.http/hypermail/historia/mar00/0093.html

[HM] Double Bubble Conjecture Proved Subject: [HM] Double Bubble Conjecture Proved From: Antreas P. Hatzipolakis ( xpolakis@otenet.gr Date: Sat Mar 18 2000 - 12:21:54 EST Next message: Hans Lausch: "Re: [HM] Copernicus' Revolutionibi" Previous message: Antreas P. Hatzipolakis: "Re: [HM] Copernicus' Revolutionibi" Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] Research Announcement, February 25, 2000 Proof of the Double Bubble Conjecture by Michael Hutchings, Frank Morgan, Manuel Ritore, and Antonio Ros History. Archimedes and Zenodorus (see [K, p. 273]) claimed and Schwarz [S] proved that the round sphere is the least-perimeter way to enclose a given volume in R3. The Double Bubble Conjecture, long assumed true (see [P, pp. 300-301], [B, p. 120]) but only recently stated as a conjecture [F1, sect. 3], says that the familiar double soap bubble on the right in Figure 1, consisting of two spherical caps separated by a spherical cap or flat disc, meeting at 120-degree angles, provides the least-perimeter way to enclose and separate two given volumes. The analogous result in R2 was

24. Historia Matematica Mailing List Archive: Re: [HM] Copernicus' Pythagoras, Ptolemy and Hilbert ; Previous message Antreas P. Hatzipolakis HM double bubble conjecture Proved ; In reply to Antreas http://sunsite.utk.edu/math_archives/.http/hypermail/historia/mar00/0094.html

Re: [HM] Copernicus' Revolutionibi Subject: Re: [HM] Copernicus' Revolutionibi From: Hans Lausch ( hans.lausch@sci.monash.edu.au Date: Sat Mar 18 2000 - 22:09:46 EST Next message: Art Johnson: "Re: [HM] L'Hopital, Pythagoras, Ptolemy and Hilbert" Previous message: Antreas P. Hatzipolakis: "[HM] Double Bubble Conjecture Proved" In reply to: Antreas P. Hatzipolakis: "Re: [HM] Copernicus' Revolutionibi" Reply: Hans Lausch: "Re: [HM] Copernicus' Revolutionibi" Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] Antreas, "Revolutionibi" is a bit tough! "Revolutionibus" is NOT a nominative singular, but an ablative plural. Or should we refer, in English, to the other two "onrevolutionses"? Salutationes, HL Hans Lausch Department of Mathematics and Statistics, Monash University, Clayton, 3168, Australia fax: +61-3-9905 4403 phone: +61-3-9905 4477 Hans.Lausch@sci.monash.edu.au Next message: Art Johnson: "Re: [HM] L'Hopital, Pythagoras, Ptolemy and Hilbert" Previous message: Antreas P. Hatzipolakis: "[HM] Double Bubble Conjecture Proved" In reply to: Antreas P. Hatzipolakis: "Re: [HM] Copernicus' Revolutionibi"

25. Lecture 4 Frank Morgan will give nine lectures on the subject of Geometric MeasureTheory and the Proof of the double bubble conjecture. Last http://zeta.msri.org/calendar/talks/TalkInfo/504/show_talk

Calendar Lecture 4 Frank Morgan (Scheduled Workshop Talk) Thursday, Jun 28, 2001 9:00 am to 10:00 am at the MSRI Lecture Hall, Mathematical Sciences Research Institute, Berkeley, California Frank Morgan will give nine lectures on the subject of Geometric Measure Theory and the Proof of the Double Bubble Conjecture. Last year Hutchings, Morgan, Ritore and Ros announced a proof of the Double Bubble Conjecture, which says that the familiar standard double soap bubble provides the least-area way to enclose and separate two given volumes of air. It was only with the advent of geometric measure theory in the 1960s that mathematicians were ready to deal with such problems involving surfaces meeting along singularities in unpredictable ways. The lectures will discuss modern, measure-theoretic definitions of "surface," compactness of spaces of surfaces, and finally the proof of the double bubble conjecture. Homework will vary from basic exercises to open problems. The text Geometric Measure Theory: A Beginner's Guide (3rd edition) by Frank Morgan will be made available, as well as additional notes and materials. (Students nominated by MSRI sponsors will receive a copy of the book on arrival. Several copies will be available for use by other participants.) There will be sessions on exercises and on open problems.

26. Electronic Research Announcements Of The AMS Hutchings, Michael Michael Hutchings; Frank Morgan; Manuel Ritoré; Antonio Ros Proofof the double bubble conjecture. Kirillov, AA AA Kirillov Family algebras. http://www-sbras.nsc.ru/EMIS/journals/ERA-AMS/era-auth-2000.html

This journal is archived by the American Mathematical Society. The master copy is available at http://www.ams.org/era/ 2000 Table of Contents - Indexed by Authors Adem, Alejandro Alejandro Adem; Jeff H. Smith On spaces with periodic cohomology Bullett, S. R. S. R. Bullett; W. J. Harvey Mating quadratic maps with Kleinian groups via quasiconformal surgery Harvey, W. J. S. R. Bullett; W. J. Harvey Mating quadratic maps with Kleinian groups via quasiconformal surgery Kirillov, A. A. A. A. Kirillov Family algebras Smith, Jeff H. Alejandro Adem; Jeff H. Smith On spaces with periodic cohomology Electronic Research Announcements of the AMS Home page t; W. J. Harvey Mating quadratic maps with Kleinian groups via quasiconformal surgery Hutchings, Michael Michael Hutchings; Frank Morgan; Manuel Ritoré; Antonio Ros Proof of the double bubble conjecture Kirillov, A. A. A. A. Kirillov Family algebras Morgan, Frank Michael Hutchings; Frank Morgan; Manuel Ritoré; Antonio Ros Proof of the double bubble conjecture Ritoré, Manuel Michael Hutchings; Frank Morgan; Manuel Ritoré; Antonio Ros Proof of the double bubble conjecture Ros, Antonio

27. Electronic Research Announcements Of The AMS quasiconformal surgery. 53A10 Michael Hutchings; Frank Morgan; Manuel Ritoré;Antonio Ros Proof of the double bubble conjecture. 53C42 Michael http://www-sbras.nsc.ru/EMIS/journals/ERA-AMS/era-msc-2000.html

This journal is archived by the American Mathematical Society. The master copy is available at http://www.ams.org/era/ 2000 Table of Contents - Indexed by Math Subject Classification A. A. Kirillov Family algebras S. R. Bullett; W. J. Harvey Mating quadratic maps with Kleinian groups via quasiconformal surgery Alejandro Adem; Jeff H. Smith On spaces with periodic cohomology Electronic Research Announcements of the AMS Home page Alejandro Adem; Jeff H. Smith On spaces with periodic cohomology A. A. Kirillov Family algebras S. R. Bullett; W. J. Harvey Mating quadratic maps with Kleinian groups via quasiconformal surgery S. R. Bullett; W. J. Harvey Mating quadratic maps with Kleinian groups via quasiconformal surgery S. R. Bullett; W. J. Harvey Mating quadratic maps with Kleinian groups via quasiconformal surgery S. R. Bullett; W. J. Harvey Mating quadratic maps with Kleinian groups via quasiconformal surgery Michael Hutchings; Frank Morgan; Manuel Ritoré; Antonio Ros Proof of the double bubble conjecture Michael Hutchings; Frank Morgan; Manuel Ritoré; Antonio Ros Proof of the double bubble conjecture Danny Calegari Alejandro Adem; Jeff H. Smith

28. Mathenomicon.net : News : Double Bubbles A proof of the double bubble conjecture has been announced at theRoseHulman Institute of Technology in Indiana, United States. http://www.cenius.net/news/news.php?ArticleID=0

29. Mathenomicon.net : News : Archive 21th March 2000 Double bubbles A proof of the double bubble conjecture has been announcedat the RoseHulman Institute of Technology in Indiana, United States. http://www.cenius.net/news/archive/default.php

Feedback Site map Archive Older mathematical and site news. Home About News Archive ... Search Return to News Index 21th March 2000 Double bubbles A proof of the Double Bubble conjecture has been announced at the Rose-Hulman Institute of Technology in Indiana, United States. 12th July 2000 Archimedes' lost writing revealed A text written by Archimedes is being restored by scientists in New York. 23rd August 2000 Cambridge raising funds for Newton writings The University of Cambridge is attempting to raise funds to buy an archive of Sir Isaac Newton's papers. Home About News Reference ... Terms and conditions Page updated: 21:24 19/12/2002 GMT Author: Mathenomicon.net

30. Department Of Mathematics - Clanton Visiting Mathematician PROOF OF THE double bubble conjecture ABSTRACT A single round soap bubble providesthe most efficient, leastarea way to enclose a given volume of air. http://math.furman.edu/activities/clanton/

DONALD H. CLANTON VISITING MATHEMATICIAN 2002-2003 CLANTON VISITING MATHEMATICIAN FRANK MORGAN Dennis Meenan '54 Third Century Professor of Mathematics Williams College AFTERNOON LECTURE PROOF OF THE DOUBLE BUBBLE CONJECTURE ABSTRACT: A single round soap bubble provides the most efficient, least-area way to enclose a given volume of air. The Double Bubble Conjecture says that the familiar double soap bubble which forms when two soap bubbles come together provides the most efficient way to enclose and separate two given volumes of air. We'll discuss the problem, the recent proof, important contributions by undergraduates, and remaining open problems. Burgiss Theater, University Center , 4:00 pm, Thursday, September 26, 2002 EVENING LECTURE THE SOAP BUBBLE GEOMETRY CONTEST ABSTRACT: A guessing contest with demonstrations, explanations, prizes, and some recent math news, including new results by undergraduates. Watkins Room, University Center , 7:30 pm, Thursday, September 26, 2002 RECEPTION Room 205

31. Department Of Mathematics - Colloquium Abstracts Proof Of the double bubble conjecture. Frank Morgan Williams College 26September 2002. ABSTRACT TBA Raymond Pearl and the Logistic Curve. http://math.furman.edu/activities/colloquium/abstracts/

COLLOQUIUM ABSTRACTS Proof Of the Double Bubble Conjecture Frank Morgan Williams College 26 September 2002 ABSTRACT : TBA Raymond Pearl and the Logistic Curve Bob Fray Furman University 10 October 2002 ABSTRACT : We will discuss some of the early history of the population ecology, then look at the development of the logistic model, beginning with Pierre-Francois Verhulst. We will conclude with an in-depth look at the campaign by Raymond Pearl to establish the logistic model as a "law" of population growth. Origins of Abstraction in Algebra, or How I Learned to Stop Worrying and Love Emmy Noether Dan Smith Furman University 24 October 2002 ABSTRACT :Algebra is essentially the study of systems of polynomial equations, although current treatments of the subject can thoroughly disguise this fact. We will consider how certain classical problems involving polynomials, such as Fermat's last theorem and the insolubility of the quintic, eventually led to the more general and abstract approach that algebraists take today. This fundamental change in perspective was in large part due to the work of Emmy Noether, who not only clarified and consolidated recent results, but more importantly demonstrated the utility of this viewpoint in breaking new ground. The Method of Archimedes John Poole Furman University 7 November 2002 ABSTRACT : When Archimedes came into the mathematical world, mathematicians knew how to find the volumes of cylinders and cones, but not spheres. We will see how Archimedes used "The Law of the Lever" to obtain a relationship between a sphere, a cylinder, and a cone, and thus how to find the volume of a sphere. Although Archimedes used only simple geometric facts, we can see how his manipulations brought him close to discovering integral calculus.

32. Double Bubble 159, 4759, 1993. Morgan, F. ``The double bubble conjecture.'' FOCUS 15,6-7, 1995. Peterson, I. ``Toil and Trouble over Double Bubbles.'' Sci. http://www.ph.tn.tudelft.nl/Internal/PHServices/Documentation/MathWorld/math/mat

Double Bubble Angles ) has the minimum Perimeter for enclosing two equal areas (Foisy 1993, Morgan 1995). See also Apple Bubble Double Bubble Conjecture Sphere-Sphere Intersection References Campbell, P. J. (Ed.). Reviews. Math. Mag. Foisy, J.; Alfaro, M.; Brock, J.; Hodges, N.; and Zimba, J. ``The Standard Double Soap Bubble in Uniquely Minimizes Perimeter.'' Pacific J. Math. Morgan, F. ``The Double Bubble Conjecture.'' FOCUS Peterson, I. ``Toil and Trouble over Double Bubbles.'' Sci. News , 101, Aug. 12, 1995. Eric W. Weisstein

33. Double Bubble Minimizes: Applications To Geometry J. Hass, M. Hutchings, and R. Schlafly, The double bubble conjecture, ElectronicResearch Announcements of the American Mathe. Society, 1995, Vol. 1, pp. http://www.lsi.upc.es/~robert/mirror/interval-comp/bubble.html

Double Bubble Minimizes: Interval Computations Help in Solving a Long-Standing Geometric Problem It is well known that of all surfaces surrounding an area with a given volume V, the sphere has the smallest area. This result explains, e.g., why a soap bubble tends to become a sphere. More than a hundred years ago, the Belgian physicist J. Plateaux asked a similar question: what is the least area surface enclosing two equal volumes? Physical experiments with bubbles seem to indicate that the desired least area surface is a "double bubble", a surface formed by two spheres (separated by a flat disk) that meet along a circle at an angle of 120 degrees. However, until 1995, it was not clear whether this is really the desired least area surface. Several other surfaces ("torus bubbles") have been proposed whose areas are pretty close to the area of the double bubble. The theorem that double bubble really minimizes was recently proven by Joel Hass from Department of Mathematics, University of California at Davis (email hass@math.ucdavis.edu

34. Clay Research Institute On The Global Theory Of Minimal Surfaces Frank Morgan will give nine lectures on the subject of Geometric Measure Theoryand the Proof of the double bubble conjecture Last year Hutchings, Morgan http://www.msri.org/ext/minimal2.html

Clay Research Institute on The Global Theory of Minimal Surfaces Program for weeks one and two The first two weeks of the 2001 Clay Mathematics Institute will include a graduate level introduction to the theory of minimal surfaces. There will be two or three lecture series and additional events and activities, including homework sessions, open problem discussions, demonstrations and instruction on computer graphics techniques. Attending will be graduate students from the MSRI sponsoring institutions and additional graduate students and researchers sponsored by the Clay Institute. Attending students are nominated by an MSRI sponsor or nominated as a Clay Mathematics Institute participant via the methods indicated in the CMI Workshop Page at the Clay Research Institute on The Global Theory of Minimal Surfaces. For the main program see the MSRI Workshop Page for the Clay Research Institute on The Global Theory of Minimal Surfaces Program for weeks one and two Main Lecture Series - Topics Frank Morgan will give nine lectures on the subject of Geometric Measure Theory and the Proof of the Double Bubble Conjecture: Last year Hutchings, Morgan, Ritore and Ros announced a proof of the Double Bubble Conjecture, which says that the familiar standard double soap bubble provides the least-area way to enclose and separate two given volumes of air. It was only with the advent of geometric measure theory in the 1960s that mathematicians were ready to deal with such problems involving surfaces meeting along singularities in unpredictable ways. The lectures will discuss modern, measure-theoretic definitions of "surface," compactness of spaces of surfaces, and finally the proof of the double bubble conjecture. Homework will vary from basic exercises to open problems. The text

35. Streaming Video - Spring 2001 June 25 July 6, 2001. Lecture Series Frank Morgan Geometric MeasureTheory and the Proof of the double bubble conjecture, Lecture 1; http://www.msri.org/publications/video/index02.html

MSRI Home Page MSRI Publications Streaming Video / Streaming Video - Spring 2001 Streaming Video - Spring 2001 Introduction Hints for Viewing Other SV Sites CDROMs and Video Tapes for sale ... Mirror Sites Welcome to the MSRI Video Archive, Click on the triangle icons to expand/contract the list. MSRI: Spring 2003 MSRI: Fall 2002 MSRI: Spring 2002 MSRI: Fall 2001 MSRI: Spring 2001 Free Probability and Non-commutative Banach Spaces January 22 - 27, 2001 L. Ge Applications of free entropy T. Cabanal-Duvillard Large deviations for Gaussian matrices and free entropies M. Stefan Some properties of free group subfactors Z-J. Ruan R. Smith Approximation properties for crossed products G. Pisier

36. BBC News | SCI/TECH | Double Bubble Is No Trouble Four mathematicians have announced a proof of the socalled double bubble conjecture- that the familiar double soap bubble is the optimal shape for enclosing http://news.bbc.co.uk/hi/english/sci/tech/newsid_685000/685243.stm

low graphics version feedback help You are in: Sci/Tech Front Page World UK ... AudioVideo Tuesday, 21 March, 2000, 12:24 GMT Double bubble is no trouble Nature will allow bubbles like this... By BBC News Online science editor Dr David Whitehouse Four mathematicians have announced a proof of the so-called Double Bubble Conjecture - that the familiar double soap bubble is the optimal shape for enclosing and separating two chambers of air. In an address to the Undergraduate Mathematics Conference at the Rose-Hulman Institute of Technology in Indiana, Frank Morgan of Williams College, Massachusetts, announced that he, Michael Hutchings of Stanford, and Manuel Ritori and Antonio Ros of Granada, had finally proved what the double soap bubble had known all along. When two round soap bubbles come together, they form a double bubble. Unless the two bubbles are the same size, the surface between them bows a bit into the larger bubble. The separating surface meets each of the two bubbles at 120 degrees. Mathematicians have expressed surprise that when two bubbles are joined in this way that the interior surface that separates them is not bowed all that much.

37. Student Papers At The NES/MAA Spring 2000 Meeting Session I double bubble conjectures Andrew Cotton, Harvard University and WilliamsCollege The double bubble conjecture in R 3 has recently been proved. http://www.southernct.edu/organizations/nesmaa/studentpapersspring2000.html

NORTHEASTERN SECTION OF THE MAA Spring 2000 MEETING June 16-17, 2000 St. Paul's School, Concord, New Hampshire Student Papers Schedule and Abstracts You can click on individual abstracts in the schedule or jump to the full set of student paper abstracts Student Papers Session I: . Double Bubble Conjectures Andrew Cotton, Harvard University and Williams College The Isoperimetric Problem on the Cylinder David Freeman, Harvard University and Williams College The Isoperimetric Problem on Singular Surfaces John Spivack, Williams College Student Papers Session II: Diophantine OlympicsWhat Does It Mean to Be a World Champion? Amanda Folsom, The University of Chicago Diophantine OlympicsCan Perfect Squares Score a Perfect 10? Alexander Pekker, Stanford University Diophantine OlympicsHow Do the Primes Factor in the Competition? Julia Snyder, Williams College Diophantine OlympicsIs It Possible for a Bad Team to Earn a Gold Medal? Rungporn Roengpitya, Williams College Student Papers Session III: Mall Time! Irma M.E.T. Servatius, Massachusetts Academy of Mathematics and Science Introduction to Geometric Dissection Nancy Peratto, Keene State College

38. Cwikel Frank Morgan Williams College Proof of the double bubble conjecture.Abstract. The double bubble conjecture says that the familiar http://www.math.princeton.edu/~seminar/2002-03-sem/MorganAbstract10-7-2002.html

Frank Morgan Williams College Proof of the Double Bubble Conjecture Abstract The Double Bubble Conjecture says that the familiar double soap bubble is the least-area way to enclose and separate two given volumes of air. I'll discuss the proof, the latest results, and open questions.

39. Seminar Week of October 7 October 11, 2002. Analysis Seminar. Topic Proof ofthe double bubble conjecture. Presenter Frank Morgan, Williams College. http://www.math.princeton.edu/~seminar/2002-03-sem/9-26-2002weekly.html

Current Seminars updated 9/26/ 2002 Week of September 26 - Discrete Mathematics Seminar Topic: Independence number and complete graph minor Presenter: Ken-ichi Kawarabayashi , Keio and Princeton University Date: Thursday, September 26, 2002, Time: 2:15 p.m., Location: Fine Hall 224 Abstract: Please click here to view abstract Geometric Analysis Seminar Topic: Perron's method for second order semilinear wave equations Presenter: Penelope Smith Lehigh University Date: Friday, September 27, 2002, Time: 3:00 p.m., Location: Fine Hall 314 Week of September 30 - October 4, 2002 Analysis Seminar Topic: Construction of solutions to the Yang-Mill Equations in higher dimensions Presenter: Simon Brendle Princeton University Date: Monday, September 30, 2002, Time: 4:00 p.m., Location: Fine Hall 314 PACM Colloquium Topic: The Level Set Method and Schroedinger's Equation Presenter: Li-Tien Cheng , University of California, San Diego Date: Monday, September 30, 2002, Time: 4:00 p.m., Location: Fine Hall 214 Abstract: The level set method has recently been succesfully applied to the construction wavefronts in geometrical optics. We extend the approach here to wavefronts found in Schroedinger's equation as well as other quantities of interest. Advantages such as an Eulerian foundation and the ability to handle multivaluedness are preserved in the extension.

40. ScienceDaily: Computers & Math News Summaries 0320 Mathematicians Prove Double Soap Bubble Had It Right Four mathematicians haveannounced a mathematical proof of the double bubble conjecture that the http://www.sciencedaily.com/news/computers_summaries.php?page=370

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