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QUANTITATIVE OSCILLATION ESTIMATES FOR ALMOST-UMBILICAL CLOSED HYPERSURFACES IN EUCLIDEAN SPACE
Published online by Cambridge University Press: 17 April 2015
Abstract
We prove ${\it\epsilon}$-closeness of hypersurfaces to a sphere in Euclidean space under the assumption that the traceless second fundamental form is ${\it\delta}$-small compared to the mean curvature. We give the explicit dependence of ${\it\delta}$ on ${\it\epsilon}$ within the class of uniformly convex hypersurfaces with bounded volume.
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- © 2015 Australian Mathematical Publishing Association Inc.
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