Displaying similar documents to “Isoperimetric Symmetry Breaking: a Counterexample to a Generalized Form of the Log-Convex Density Conjecture”

The double bubble conjecture.

Hass, Joel, Hutchings, Michael, Schlafly, Roger (1995)

Electronic Research Announcements of the American Mathematical Society [electronic only]

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Symmetry problems 2

N. S. Hoang, A. G. Ramm (2009)

Annales Polonici Mathematici

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Some symmetry problems are formulated and solved. New simple proofs are given for some symmetry problems studied earlier. One of the results is as follows: if a single-layer potential of a surface, homeomorphic to a sphere, with a constant charge density, is equal to c/|x| for all sufficiently large |x|, where c > 0 is a constant, then the surface is a sphere.

Isoperimetric Regions in Rnwith Density rp

Wyatt Boyer, Bryan Brown, Gregory R. Chambers, Alyssa Loving, Sarah Tammen (2016)

Analysis and Geometry in Metric Spaces

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We show that the unique isoperimetric regions in Rn with density rp for n ≥ 3 and p > 0 are balls with boundary through the origin.

Planar vector field versions of Carathéodory's and Loewner's conjectures.

Carlos Gutiérrez, Federico Sánchez Bringas (1997)

Publicacions Matemàtiques

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Let r = 3, 4, ... , ∞, ω. The Cr-Carathéodory's Conjecture states that every Cr convex embedding of a 2-sphere into R3 must have at least two umbilics. The Cr-Loewner's conjecture (stronger than the one of Carathéodory) states that there are no umbilics of index bigger than one. We show that these two conjectures are equivalent to others about planar vector fields. For instance, if r ≠ ω, Cr...