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Explicit rigidity of almost-umbilical hypersurfaces

Roth, Julien and Scheuer, Julian 2019. Explicit rigidity of almost-umbilical hypersurfaces. Asian Journal of Mathematics 22 (6) , pp. 1075-1088. 10.4310/AJM.2018.v22.n6.a5

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We give an explicit estimate of the distance of a closed, connected, oriented and immersed hypersurface of a space form to a geodesic sphere and show that the spherical closeness can be controlled by a power of an integral norm of the traceless second fundamental form, whenever the latter is sufficiently small. Furthermore we use the inverse mean curvature flow in the hyperbolic space to deduce the best possible order of decay in the class of C∞-bounded hypersurfaces of the Euclidean space. Keywords pinching, almost-umbilical hypersurfaces, inverse mean curvature flow

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Publisher: International Press
ISSN: 1093-6106
Date of First Compliant Deposit: 8 October 2020
Date of Acceptance: 3 March 2017
Last Modified: 07 Dec 2020 18:40

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