Characterization of isoperimetric sets inside almost-convex cones

TL;DR

This paper characterizes isoperimetric regions within almost-convex cones, demonstrating that these regions are intersections of the cone with centered balls, extending known results from convex cones.

Contribution

It extends the characterization of isoperimetric sets from convex cones to almost-convex cones, providing a broader understanding of geometric optimization in these regions.

Findings

Isoperimetric sets in almost-convex cones are intersections with centered balls.

The characterization parallels that of convex cones, confirming similar geometric properties.

Provides a mathematical foundation for further studies in geometric analysis within such cones.

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.