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Low Index Capillary Minimal Surfaces in Riemannian 3-Manifolds

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Abstract

We prove a local rigidity result for infinitesimally rigid capillary surfaces in some Riemannian 3-manifolds with mean-convex boundary. We also derive bounds on the genus, number of boundary components and area of any compact two-sided capillary minimal surface with low index under certain assumptions on the curvature of the ambient manifold and of its boundary.

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Acknowledgements

The author would like to thank Paolo Piccione for his constant support and encouragement during the period when this article was written and revised, and for countless fruitful mathematical conversations. He also expresses sincere gratitude to Lucas Ambrozio for valuable comments on this work. Additionally, he thanks Izabella Freitas and Jackeline Conrado for the figures in this paper. The author was partially supported by Grant 2017/22704-0, São Paulo Research Foundation (FAPESP).

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  1. Departamento de Matemática, Instituto de Matemática e Estatística, Universidade de São Paulo, R. do Matão 1010, São Paulo, SP, 05508-900, Brazil

    Eduardo Rosinato Longa

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  1. Eduardo Rosinato Longa
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The author was partially supported by Grant 2017/22704-0, São Paulo Research Foundation (FAPESP)

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Rosinato Longa, E. Low Index Capillary Minimal Surfaces in Riemannian 3-Manifolds. J Geom Anal 32, 143 (2022). https://doi.org/10.1007/s12220-022-00883-6

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