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QUANTITATIVE OSCILLATION ESTIMATES FOR ALMOST-UMBILICAL CLOSED HYPERSURFACES IN EUCLIDEAN SPACE

Published online by Cambridge University Press:  17 April 2015

JULIAN SCHEUER
Affiliation:
Ruprecht-Karls-Universität, Institut für Angewandte Mathematik, Im Neuenheimer Feld 294, 69120 Heidelberg, Germany email scheuer@math.uni-heidelberg.de
Corresponding
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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.

Type
Research Article
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

References

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QUANTITATIVE OSCILLATION ESTIMATES FOR ALMOST-UMBILICAL CLOSED HYPERSURFACES IN EUCLIDEAN SPACE
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QUANTITATIVE OSCILLATION ESTIMATES FOR ALMOST-UMBILICAL CLOSED HYPERSURFACES IN EUCLIDEAN SPACE
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