Uniqueness of Critical Points of the Anisotropic Isoperimetric Problem for Finite Perimeter Sets

2019/08/26 by Antonio De Rosa, Sławomir Kolasiński, Mario Santilli
Mathematics · #Analytic and geometric function theory #Anisotropy #Boundary (topology) #Class (philosophy) #Disjoint sets #Isoperimetric inequality #Mathematical Approximation and Integration #Nonlinear Partial Differential Equations #Perimeter #RADIUS #Surface (topology) #Uniqueness #math.AP #math.DG #msc:49Q10 #msc:49Q20 #msc:53A10

paper · pdf · doi:10.1007/s00205-020-01562-y

arxiv created 2019/08/26 · openalex created_date 2019/08/29 · openalex publication_date 2020/08/17 · arxiv updated 2020/10/28 · openalex updated_date 2026/08/05

Abstract

Given an elliptic integrand of class \mathscrC³ , 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.

Citations

• On the First Variation of a Varifold
• Normal bundle and Almgren’s geometric inequality for singular varieties of bounded mean curvature