# American Institute of Mathematical Sciences

January  2017, 37(1): 1-14. doi: 10.3934/dcds.2017001

## Characterization of isoperimetric sets inside almost-convex cones

 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

Received  April 2016 Revised  May 2016 Published  November 2016

Fund Project: 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.

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.

Citation: Eric Baer, Alessio Figalli. Characterization of isoperimetric sets inside almost-convex cones. Discrete & Continuous Dynamical Systems - A, 2017, 37 (1) : 1-14. doi: 10.3934/dcds.2017001
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