Characterization of isoperimetric sets inside almost-convex cones

Eric Baer; Alessio Figalli

doi:10.3934/dcds.2017001

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2017, Volume 37, Issue 1: 1-14. Doi: 10.3934/dcds.2017001 open access

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Characterization of isoperimetric sets inside almost-convex cones

Eric Baer^1, and
Alessio Figalli^2, ,

1.
Department of Mathematics, University of Wisconsin Madison, 480 Lincoln Dr, Madison, WI 53706, USA
2.
The University of Texas at Austin, Mathematics Department, 2515 Speedway Stop C1200, Austin, TX 78712, USA

* Corresponding author:figalli@math.utexas.edu
* Corresponding author:figalli@math.utexas.edu

Received: March 31, 2016

Revised: April 30, 2016

Published: September 2017

The work of E.B. was partially supported by the National Science Foundation under Award Nos. DMS-1204557 and DMS-1147523. The work of A.F. was partially supported by the National Science Foundation under Award Nos. DMS-1262411 and DMS-1361122

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Abstract

In this note we characterize isoperimetric regions inside almost-convex cones. More precisely, as in the case of convex cones, we show that isoperimetric sets are given by intersecting the cone with a ball centered at the origin.

Keywords:

Isoperimetric inequality,
almost-convex cones.

Mathematics Subject Classification: Primary:49Q20;Secondary:49K10.

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