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arXiv · 1404.2525

Quantitative oscillation estimates for almost-umbilical closed hypersurfaces in Euclidean space

Julian Scheuer
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Abstract

We prove $ε$-closeness of hypersurfaces to a sphere in Euclidean space under the assumption that the traceless second fundamental form is $δ$-small compared to the mean curvature. We give the explicit dependence of $δ$ on $ε$ within the class of uniformly convex hypersurfaces with bounded volume.

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Julian Scheuer. 2014-04-09. Quantitative oscillation estimates for almost-umbilical closed hypersurfaces in Euclidean space. https://doi.org/10.1017/s0004972715000222

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