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

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2013

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Scheuer, Julian

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http://nbn-resolving.de/urn:nbn:de:bsz:352-264019
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http://arxiv.org/abs/1307.5764

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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-Warner to convex C2-hypersurfaces. We apply these results to prove C{1,\beta}-convergence of inverse F-curvature flows in the sphere to an equator in Sn+1 for embedded, closed, orientable, 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 Alexandrov-Fenchel type inequalities and solve isoperimetric type problems in the sphere.

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510 Mathematik

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ISO 690MAKOWSKI, Matthias, Julian SCHEUER, 2013. Rigidity results, inverse curvature flows and Alexandrov-Fenchel type inequalities in the sphere
BibTex
@unpublished{Makowski2013Rigid-26401,
  year={2013},
  title={Rigidity results, inverse curvature flows and Alexandrov-Fenchel type inequalities in the sphere},
  author={Makowski, Matthias and Scheuer, Julian}
}
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