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

Scheuer, Julian ORCID: https://orcid.org/0000-0003-2664-1896 2015. Quantitative oscillation estimates for almost-umbilical closed hypersurfaces in euclidean space. Bulletin of the Australian Mathematical Society 92 (1) , pp. 133-144. 10.1017/S0004972715000222

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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.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Publisher:	Cambridge University Press
ISSN:	0004-9727
Funders:	Deutsche Forschungsgemeinschaft (German Research Foundation, DFG)
Date of First Compliant Deposit:	15 September 2020
Date of Acceptance:	13 January 2015
Last Modified:	25 Nov 2024 07:15
URI:	https://orca.cardiff.ac.uk/id/eprint/134860

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