QUANTITATIVE OSCILLATION ESTIMATES FOR ALMOST-UMBILICAL CLOSED HYPERSURFACES IN EUCLIDEAN SPACE
2015 ◽
Vol 92
(1)
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pp. 133-144
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Keyword(s):
The Mean
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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.