Alexandrov's theorem revisited

TL;DR

This paper revisits Alexandrov's theorem, demonstrating that in the context of sets with finite perimeter, balls uniquely serve as the critical points of the perimeter functional under volume constraints.

Contribution

The work provides a new perspective or proof that balls are the only volume-constrained critical points among finite perimeter sets, refining previous understanding.

Findings

Balls are the only volume-constrained critical points of the perimeter functional.

The result applies specifically to sets of finite perimeter.

The paper offers a revisited proof or perspective on Alexandrov's theorem.

Abstract

We show that among sets of finite perimeter balls are the only volume-constrained critical points of the perimeter functional.