Uniqueness of critical points of the anisotropic isoperimetric problem for finite perimeter sets

Abstract

Given an elliptic integrand of class ${\mathcal{C}}^3$, we prove that finite unions of disjoint 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.

References in corpus (8)

• Alexandrov's theorem revisited
• Bubbling with $L^2$-almost constant mean curvature and an Alexandrov-type theorem for crystals
• Rectifiability and approximate differentiability of higher order for sets
• Equivalence of the ellipticity conditions for geometric variational problems
• Fine properties of the curvature of arbitrary closed sets
• The spherical image of singular varieties of bounded mean curvature
• Pointwise differentiability of higher order for sets
• A geometric second-order-rectifiable stratification for closed subsets of Euclidean space

Cited by in corpus (6)

• Alexandrov's theorem for anisotropic capillary hypersurfaces in the half-space
• Absence of bubbling phenomena for non convex anisotropic nearly umbilical and quasi Einstein hypersurfaces
• Quantitative Alexandrov theorem and asymptotic behavior of the volume preserving mean curvature flow
• Second order rectifiability of varifolds of bounded mean curvature
• The double and triple bubble problem for stationary varifolds: the convex case
• $C^{1,1}$-rectifiability and Heintze-Karcher inequality on ${\mathbf{S}}^{n+1}$