21. Www.math.vanderbilt.edu an MAA article Double Bubble Conjecture, proved. an NSF article Double Soap Bubbles Proof Positive of Optimal Geometry references Proof of the Double Bubble Conjecture. http://www.math.vanderbilt.edu/~mathclub/OldSite/index.html

About us The Vanderbilt Math Club was created in order to provide a place where undergraduate students, grad students, postdocs, and professors can get to know each other on a more informal level outside of the classroom. Students can find mentoring, make contacts, meet fellow math enthusiasts, and learn invaluable information about undergraduate opportunities, future careers, and the fascinating, beautiful world of mathematics. Everyone interested in mathematics is invited, from math majors to engineering majors to art majors. Announcements The inaugural Vanderbilt High School Math Competition took place on April 1, 2006. For the competition results, please http://www.math.vanderbilt.edu/~mathclub/competition/ Schedule of Events Apr 19, 6:00pm room SC1432 Final math club meeting of the semester! speaker: Dr. Dan Guralnik, Vanderbilt University The skies in the limit: geometric ideas of infinity Imagine yourself standing on some dusty, sun-dried road, staring at the horizon and waiting for someone approaching from the horizon to pick you up. It's hot, and your brain produces hallucinations...your math teacher, talking about railroad tracks and imaginary points at infinity, where those tracks meet. In my talk I will discuss different ideas of drawing `boundaries at infinity' or `skies' for different mathematical models of the world around us. What shape are the skies above you? Apr 12, 6:00pm room SC1432

22. THE DOUBLE BUBBLE CONJECTURE (Communicated By Richard Schoen) 1 File Format PDF/Adobe Acrobat Quick View http://aimsciences.org/journals/pdfs.jsp?paperID=2365&mode=abstract

23. Proof Of The Double Bubble Conjecture In R PROOF OF THE DOUBLE BUBBLE CONJECTURE INR4 AND CERTAIN HIGHER DIMENSIONAL CASES Proof of the Double Bubble Conjecture in R http://nyjm.albany.edu:8000/PacJ/p/2003/208-2-9.pdf

24. GEOMETRIC MEASURE THEORY AND THE PROOF OF THE DOUBLE BUBBLE File Format PDF/Adobe Acrobat Quick View http://www.ugr.es/~ritore/preprints/course.pdf

25. Roger Schlafly - Conservapedia THE DOUBLE BUBBLE CONJECTURE; Double bubbles minimize; Interactive formula compiler and range estimator; Modular exponentiation and reduction device and method http://www.conservapedia.com/Roger_Schlafly

Roger Schlafly From Conservapedia Jump to: navigation search Roger Schlafly Roger Schlafly is an independent computer programmer. In 1980, he received a PhD in mathematics from University of California at Berkeley, under Abel prize laureate Isadore Singer. He is the son of conservative activist Phyllis Schlafly and the brother of John Schlafly and Conservapedia founder Andrew Schlafly His blog is called Dark Buzz Rigidity of Pseudoconformal Connections Universal connections THE DOUBLE BUBBLE CONJECTURE ... Universal connections: the local problem Retrieved from " http://www.conservapedia.com/Roger_Schlafly Category Scientists Views Page talk page View source History Personal tools Log in Search Popular Links Main Page Educational Index Debate Topics Recent changes ... Random page Help Help Index Statistics Conservapedia Commandments World History World History Lectures World History Homework Edit Console What links here Related changes Special pages Printable version ... Permanent link This page was last modified on 16 August 2008, at 14:11. This page has been accessed 5,361 times.

26. PROOF OF THE DOUBLE BUBBLE CONJECTURE electronic research announcements of the american mathematical society volume 6, pages 45{49 (july 17,2000) s10796762(00)00079-2 proof of the double bubble conjecture michaelhutchings http://math.berkeley.edu/~hutching/pub/db2ann/db2ann.pdf

27. Soap Bubble Mathematicians Prove Double Soap Bubble Had It Right (March 20, 2000) — Four mathematicians have announced a mathematical proof of the Double Bubble Conjecture that the familiar http://www.sciencedaily.com/articles/s/soap_bubble.htm

Science Reference Share Blog Print Email Bookmark Soap bubble A soap bubble is a very thin film of soap water that forms a hollow sphere with an iridescent surface. See also: Nature of Water Transportation Science Graphene Nuclear Energy Soap bubbles usually last for only a few moments and then burst either on their own or on contact with another object. They are often used as a children's plaything, but their usage in artistic performances shows that they can be fascinating for adults too. Soap bubbles can help to solve complex mathematical problems of space, as they will always find the smallest surface area between points or edges. A bubble can exist because the surface layer of a liquid (usually water) has a certain surface tension, which causes the layer to behave somewhat like an elastic sheet. However, a bubble made with a pure liquid alone is not stable and a dissolved surfactant such as soap is needed to stabilize a bubble. A common misconception is that soap increases the water's surface tension. Actually soap does the exact opposite, decreasing it to approximately one third the surface tension of pure water.

28. Involve, A Journal Of Mathematics Vol. 2, No. 5, 2009 Proof of the planar double bubble conjecture using metacalibration methods Rebecca Dorff, Gary Lawlor, Donald Sampson and Brandon Wilson http://pjm.math.berkeley.edu/involve/2009/2-5/p09.xhtml

Vol. 2, No. 5, 2009 Download this article For screen For printing Recent Issues Volume 3, Issue 2 Volume 3, Issue 1 Volume 2, Issue 5 Volume 2, Issue 4 ... Volume 1, Issue 1 The Journal Cover Page Editorial Board About the Journal Scientific Advantages ... Proof of the planar double bubble conjecture using metacalibration methods Rebecca Dorff, Gary Lawlor, Donald Sampson and Brandon Wilson Vol. 2 (2009), No. 5, 611–628 Abstract We prove the double bubble conjecture in R : that the standard double bubble in R is boundary length-minimizing among all figures that separately enclose the same areas. Our independent proof is given using the new method of metacalibration , a generalization of traditional calibration methods useful in minimization problems with fixed volume constraints. Keywords calibration, metacalibration, double bubble, isoperimetric, optimization Mathematical Subject Classification Primary: 49Q05, 49Q10, 53A10

29. [0705.1601] Proof Of The Double Bubble Conjecture In R^n by BW Reichardt 2007 - Cited by 2 - Related articles http://arxiv.org/abs/0705.1601

arXiv.org math Search or Article-id Help Advanced search All papers Titles Authors Abstracts Full text Help pages Full-text links: Download: PDF PostScript Other formats Current browse context: math.MG new recent Change to browse by: math NASA ADS Bookmark what is this? Mathematics > Metric Geometry Title: Proof of the Double Bubble Conjecture in R^n Authors: Ben W. Reichardt (Submitted on 11 May 2007) Abstract: The least-area hypersurface enclosing and separating two given volumes in R^n is the standard double bubble. Comments: 20 pages, 22 figures Subjects: Metric Geometry (math.MG) MSC classes: Journal reference: J. Geom. Anal. 18(1):172-191, 2008 DOI 10.1007/s12220-007-9002-y Cite as: arXiv:0705.1601v1 [math.MG] Submission history From: Ben Reichardt [ view email Fri, 11 May 2007 08:15:52 GMT (1000kb) Which authors of this paper are endorsers? Link back to: arXiv form interface contact

30. THE DOUBLE BUBBLE CONJECTURE - Microsoft Academic Search Authors JOEL HASS, MICHAEL HUTCHINGS, ROGER SCHLAFLY. Citations 15 http://academic.research.microsoft.com/Paper/3881861.aspx

var SiteRoot = 'http://academic.research.microsoft.com'; SHARE Author Conference Journal Year Look for results that meet for the following criteria: since equal to before Publication THE DOUBLE BUBBLE CONJECTURE Edit THE DOUBLE BUBBLE CONJECTURE Citations: 15 JOEL HASS MICHAEL HUTCHINGS ROGER SCHLAFLY The classical isoperimetric inequality states that the surface of smallest area enclosing a given volume in R3 is a sphere. We show that the least area surface enclosing two equal volumes is a double bubble, a surface made of two pieces of round spheres separated by a flat disk, meeting along a single circle at an angle of 2�/3. View or Download The following links allow you to view and download full papers. These links are maintained by other sources not affiliated with Microsoft Academic Search. www.ams.org reference.kfupm.edu.sa math.berkeley.edu eprints.kfupm.edu.sa ... J. Eells Published in 1987. The structure of singularities in soap-bubble-like and soap-ˉlm-like minimal surfaces Citations: 39 Jean E. Taylor

31. Frank Morgan Facts - Freebase He is most famous for proving the double bubble conjecture, that the minimumsurface-area enclosure of two given volumes is formed by three spherical patches meeting at 120-degree http://www.freebase.com/view/m/04y9cww

32. THE DOUBLE BUBBLE CONJECTURE (Communicated By Richard Schoen) 1 File Format PDF/Adobe Acrobat Quick View http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.81.2669&rep=rep1&am

33. Proof Of The Double Bubble Conjecture In R Sup 4 /sup And Certain File Format PDF/Adobe Acrobat Quick View http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.119.5987&rep=rep1&a

34. PROOF OF THE DOUBLE BUBBLE CONJECTURE INRn arXiv0705.1601v 1 math.MG 11 May 2007 PROOF OF THE DOUBLE BUBBLE CONJECTURE INR n BENW. REICHARDT Abstract. The leastarea hypersurface enclosing and separating two given volumes in http://arxiv.org/pdf/0705.1601.pdf

35. Proof Of The Double Bubble Conjecture File Format PDF/Adobe Acrobat Quick View http://hera.ugr.es/doi/15086987.pdf

36. PROOF OF THE DOUBLE BUBBLE CONJECTURE Theorem 1.1. In R File Format Adobe PostScript View as HTML http://math.berkeley.edu/~hutching/pub/db2ann/db2ann.ps

37. Double Bubble Conjecture Double Bubble Conjecture General Math discussion what is it and how was it prooved? http://www.physicsforums.com/showthread.php?t=1086

38. Proof Of The Double Bubble Conjecture electronic research announcements of the american mathematical society volume 6, pages 45–49 (july 17, 2000) s 10796762(00)00079-2. proof of the double bubble conjecture michael http://www.scribd.com/doc/35512104/Proof-of-the-Double-Bubble-Conjecture

39. Proof Of The Double Bubble Conjecture - Microsoft Academic Search Authors Michael Hutchings, Frank Morgan, Manuel Ritore, Antonio Ros. Citations 29 http://academic.research.microsoft.com/Paper/4197866.aspx

var SiteRoot = 'http://academic.research.microsoft.com'; SHARE Author Conference Journal Year Look for results that meet for the following criteria: since equal to before Publication Proof of the Double Bubble Conjecture Edit Proof of the Double Bubble Conjecture Citations: 29 Michael Hutchings Frank Morgan Manuel Ritore ... Antonio Ros We prove that the standard double bubble provides the least-area way to enclose and separate two regions of prescribed volume in R3. Published in 2002. View or Download The following links allow you to view and download full papers. These links are maintained by other sources not affiliated with Microsoft Academic Search. www.ugr.es math.berkeley.edu www.aimsciences.org Reference ... J. Eschenburg Published in 1988. Sur le volume minimal de R Citations: 9 C. Bavard P. Pansu Published in 1986. THE DOUBLE BUBBLE PROBLEM IN SPHERICAL SPACE AND HYPERBOLIC SPACE Citations: 3 ANDREW COTTON DAVID FREEMAN Published in 2002.

40. JSTOR: An Error Occurred Setting Your User Cookie Your browser may not have a PDF reader available. Google recommends visiting our text version of this document. http://www.jstor.org/stable/3062123

Skip to main content Login Help Contact Us Trusted archives for scholarship Search Basic Advanced Citation Locator ... Profile An Error Occurred Setting Your User Cookie The JSTOR site requires that your browser allows JSTOR ( http://www.jstor.org ) to set and modify cookies. JSTOR uses cookies to maintain information that will enable access to the archive and improve the response time and performance of the system. Any personal information, other than what is voluntarily submitted, is not extracted in this process, and we do not use cookies to identify what other websites or pages you have visited. JSTOR is part of ITHAKA, a not-for-profit organization helping the academic community use digital technologies to preserve the scholarly record and to advance research and teaching in sustainable ways. Terms and Conditions Accessibility

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