# Uniqueness of critical points of the anisotropic isoperimetric problem

## Antonio De Rosa (UMD)

created by gelli on 22 Apr 2020
modified on 23 Apr 2020

6 may 2020 -- 17:30   [open in google calendar]

Abstract. The anisotropic isoperimetric problem consists in enclosing a prescribed volume in a closed hypersurface with least anisotropic energy. Although its solutions, referred to as Wulff shapes, are well understood, the characterization of the associated critical points is more subtle. In this talk we present a uniqueness result: Given an elliptic integrand of class $C^3$, we prove that finite unions of disjoint (but possibly mutually tangent) open Wulff shapes with equal radii are the only volume-constrained critical points of the anisotropic surface energy among all sets with finite perimeter and reduced boundary almost equal to its closure. To conclude, we will discuss a quantitative stability for this rigidity theorem. Joint work with Mario Santilli and Slawomir Kolasinski.