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Geometry of compact quasi-Einstein manifolds with boundary

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Abstract

In this article, we study the geometry of compact quasi-Einstein manifolds with boundary. We establish sharp boundary estimates for compact quasi-Einstein manifolds with boundary that improve some previous results. Moreover, we obtain a characterization theorem for such manifolds in terms of the surface gravity of the boundary components, which leads to a new sharp geometric inequality. In addition, we prove a boundary estimate for compact quasi-Einstein manifolds with (possibly disconnected) boundary in terms of the Brown–York mass.

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Acknowledgements

The authors want to thank the referee for the careful reading, relevant remarks and valuable suggestions. The third named author would like to thank the Instituto de Matemática—Universidade Federal Fluminense, where part of this work was carried out, for the fruitful research environment. He is grateful to Detang Zhou for the warm hospitality and enlightening conversations on the related topics.

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Authors and Affiliations

  1. Instituto de Ciências Exatas e da Natureza, UNILAB, Rua José Franco de Oliveira, Redenção, CE, 62790-970, Brazil

    Rafael Diógenes

  2. Instituto Federal do Ceará - IFCE, Campus Maracanaú, Av. Parque Central, Maracanaú, CE, 61939-140, Brazil

    Tiago Gadelha

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

    Ernani Ribeiro Jr.

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  1. Rafael Diógenes
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  2. Tiago Gadelha
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  3. Ernani Ribeiro Jr.
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Correspondence to Ernani Ribeiro Jr..

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T. Gadelha was partially supported by FUNCAP/Brazil.

E. Ribeiro was partially supported by CNPq/Brazil [Grants: 305410/2018-0 & 160002/2019-2] and CAPES/Brazil - Finance Code 001.

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Diógenes, R., Gadelha, T. & Ribeiro, E. Geometry of compact quasi-Einstein manifolds with boundary. manuscripta math. 169, 167–183 (2022). https://doi.org/10.1007/s00229-021-01340-4

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