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On stable constant mean curvature surfaces with free boundary

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Abstract

Ros and Vergasta (Geom Dedicata 56:19–33, 1995) proved, among others interesting results, a theorem which states that an immersed orientable compact stable constant mean curvature surface \(\Sigma \) with free boundary in a closed ball \(B\subset \mathbb {R}^3\) must be a planar equator, a spherical cap or a surface of genus 1 with at most two boundary components. In this article, by using a modified Hersch type balancing argument, we complete their work by proving that \(\Sigma \) cannot have genus 1.

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Acknowledgements

The author would like to thank André Neves and Fernando Codá Marques for many useful mathematical conversations. The author was financially supported by CNPq-Brazil and FAPEMA/CNPq.

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  1. Ivaldo Nunes

    Present address: Departamento de Matemática, Universidade Federal do Maranhão, Campus do Bacanga, São Luís, MA, Brasil

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  1. Departament of Mathematics, Imperial College London, South Kensington Campus, London, UK

    Ivaldo Nunes

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  1. Ivaldo Nunes
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Nunes, I. On stable constant mean curvature surfaces with free boundary. Math. Z. 287, 473–479 (2017). https://doi.org/10.1007/s00209-016-1832-5

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