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QUANTITATIVE OSCILLATION ESTIMATES FOR ALMOST-UMBILICAL CLOSED HYPERSURFACES IN EUCLIDEAN SPACE
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 92 / Issue 1 / August 2015
- Published online by Cambridge University Press:
- 17 April 2015, pp. 133-144
- Print publication:
- August 2015
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- Article
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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.
