Calculus of Variations and Geometric Measure Theory

S. Wang

Round spheres are Hausdorff stable under small perturbation of entropy

created by wang on 13 Nov 2020


Published Paper

Inserted: 13 nov 2020
Last Updated: 13 nov 2020

Journal: Journal für die reine und angewandte Mathematik
Volume: 2020
Pages: 261–280
Year: 2017

ArXiv: 1704.08900 PDF


We show that if the entropy of any closed hypersurface is close to that of a round hyper-sphere, then it is close to a round sphere in Hausdorff distance. Generalizing the result of \cite{BW1} to higher dimensions.