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An Alexandrov–Fenchel-type inequality for hypersurfaces in the sphere

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Abstract

We find a monotone quantity along the inverse mean curvature flow and use it to prove an Alexandrov–Fenchel-type inequality for strictly convex hypersurfaces in the n-dimensional sphere, \(n \ge 3\).

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Authors and Affiliations

  1. Departamento de Matemática, Universidade Federal do Ceará, Campus do Pici, Av. Humberto Monte, s/n, Bloco 914, Fortaleza, CE, 60455-760, Brazil

    Frederico Girão & Neilha M. Pinheiro

Authors
  1. Frederico Girão
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  2. Neilha M. Pinheiro
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Corresponding author

Correspondence to Frederico Girão.

Additional information

Frederico Girão was partially supported by CNPq, Brazil, Grant Number 483844/2013-6.

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Girão, F., Pinheiro, N.M. An Alexandrov–Fenchel-type inequality for hypersurfaces in the sphere. Ann Glob Anal Geom 52, 413–424 (2017). https://doi.org/10.1007/s10455-017-9562-4

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  • DOI: https://doi.org/10.1007/s10455-017-9562-4

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