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Rigidity of Free Boundary Minimal Disks in Mean Convex Three-Manifolds

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Abstract

The purpose of this article is to study rigidity of free boundary minimal two-disks that locally maximize the modified Hawking mass on a Riemannian three-manifold with a positive lower bound on its scalar curvature and mean convex boundary. Assuming the strict stability of \(\Sigma \), we prove that a neighborhood of it in M is isometric to one of the half de Sitter–Schwarzschild space.

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Acknowledgements

The authors would like to thank the referee for the valuable suggestions that improved the paper. They would also like to extend special thanks to Cicero T. Cruz for his very helpful comments during the preparation of this article. The first and second authors were partially supported by CNPq/Brazil [Grant: 422900/2021-4], while the third author was partially supported by PAPG/FAPEPI/ Brazil [Grant: 030/2021].

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Authors and Affiliations

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

    Rondinelle Batista, Barnabé Lima & João Silva

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  1. Rondinelle Batista
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  2. Barnabé Lima
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  3. João Silva
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Correspondence to Rondinelle Batista.

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Batista, R., Lima, B. & Silva, J. Rigidity of Free Boundary Minimal Disks in Mean Convex Three-Manifolds. J Geom Anal 34, 279 (2024). https://doi.org/10.1007/s12220-024-01727-1

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