Round spheres are Hausdorff stable under small perturbation of entropy

Abstract

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.

All comments welcome!

References in corpus (2)

• Topology of Closed Hypersurfaces of Small Entropy
• Hausdorff Stability of the Round Two-Sphere Under Small Perturbations of the Entropy