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Geometric inequalities for critical metrics of the volume functional

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Abstract

In this article, we investigate the geometry of critical metrics of the volume functional on an n-dimensional compact manifold with (possibly disconnected) boundary. We establish sharp estimates to the mean curvature and area of the boundary components of critical metrics of the volume functional on a compact manifold. In addition, localized version estimates to the mean curvature and area of the boundary of critical metrics are also obtained.

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Authors and Affiliations

  1. Departamento de Matemática Campus Petrônio Portella, Universidade Federal do Piauí - UFPI, Teresina / PI, 64049-550, Brazil

    H. Baltazar & R. Batista

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

    E. Ribeiro Jr.

Authors
  1. H. Baltazar
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  2. R. Batista
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  3. E. Ribeiro Jr.
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Correspondence to E. Ribeiro Jr..

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H. Baltazar was partially supported by FAPEPI/Brazil (Grant: 007/2018)

R. Batista was partially supported by CNPq/Brazil (Grant: 310881/2017-0)

E. Ribeiro was partially supported by CNPq/Brazil (Grant: 305410/2018-0 and 160002/2019-2), PRONEX-FUNCAP/CNPq/Brazil, CAPES/ Brazil - Finance Code 001.

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Baltazar, H., Batista, R. & Ribeiro, E. Geometric inequalities for critical metrics of the volume functional. Annali di Matematica 201, 1463–1480 (2022). https://doi.org/10.1007/s10231-021-01164-9

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  • DOI: https://doi.org/10.1007/s10231-021-01164-9

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