Round spheres are Hausdorff stable under small perturbation of entropy

2017/04/28 by Shengwen Wang, Wang, Shengwen
Mathematics · #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1704.08900

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 \citeBW1 to higher dimensions.

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