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Annals of Global Analysis and Geometry

, Volume 55, Issue 2, pp 281–298 | Cite as

Capacity inequalities and rigidity of cornered/conical manifolds

  • Tiarlos CruzEmail author
Article
  • 64 Downloads

Abstract

We prove capacity inequalities involving the total mean curvature of hypersurfaces with boundary in convex cones and the mass of asymptotically flat manifolds with non-compact boundary. We then give the analogous of Pölia–Szegö-, Alexandrov–Fenchel- and Penrose-type inequalities in this setting. Among the techniques used in this paper are the inverse mean curvature flow for hypersurfaces with boundary.

Keywords

Capacity Inverse mean curvature flow Rigidity Riemannian penrose inequality Convex cone 

Notes

Acknowledgements

The author would like to thank Professor A. Neves for providing a wonderful scientific environment when he was visiting Imperial College London and where the first drafts of this work were written. Also, he thanks an anonymous referee for suggestions which helped substantially improve the presentation and L. Pessoa for bringing [13] to my attention. While at Imperial College, I was supported by CNPq/Brazil.

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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Universidade Federal de Alagoas, Instituto de MatemáticaMaceióBrazil

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