Rigidity results, inverse curvature flows and Alexandrov-Fenchel type inequalities in the sphere

Makowski, Matthias and Scheuer, Julian ORCID: https://orcid.org/0000-0003-2664-1896 2016. Rigidity results, inverse curvature flows and Alexandrov-Fenchel type inequalities in the sphere. The Asian Journal of Mathematics 20 (5) , p. 869. 10.4310/AJM.2016.v20.n5.a2

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Abstract

We prove a rigidity result in the sphere which allows us to generalize a result about smooth convex hypersurfaces in the sphere by Do Carmo and Warner to convex C 2 C2 -hypersurfaces. We apply these results to prove C 1,β C1,β -convergence of inverse F F -curvature flows in the sphere to an equator in S n+1 Sn+1 for embedded, closed and strictly convex initial hypersurfaces. The result holds for large classes of curvature functions including the mean curvature and arbitrary powers of the Gauss curvature. We use this result to prove some Alexandrov–Fenchel type inequalities.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Publisher:	International press
ISSN:	1093-6106
Date of First Compliant Deposit:	21 April 2020
Date of Acceptance:	28 April 2015
Last Modified:	17 Nov 2024 07:45
URI:	https://orca.cardiff.ac.uk/id/eprint/131154

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