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Stability of Capillary Hypersurfaces with Planar Boundaries

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Abstract

We prove that, in a Euclidean domain bounded by hyperplanes having linearly independent normals, a connected oriented compact immersed stable capillary hypersurface \(M^n\) disjoint from the edges of the domain and with the contact angles belonging to \([\pi /2,\pi ]\) must be part of a sphere, if \(\partial M\) is embedded for \(n=2\), or \(\partial M\) is convex in the hyperplane for \(n\ge 3\). By applying a similar argument, we also discuss two other cases where a stable capillary hypersurface must be part of a sphere.

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Acknowledgments

The authors would like to thank the referee for his/her careful reading of the paper and many valuable suggestions and comments which made this paper better and more readable. The research of the authors was supported by NSFC No. 11271214

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Authors and Affiliations

  1. Department of mathematical sciences, Tsinghua University, 100084, Beijing, People’s Republic of China

    Haizhong Li & Changwei Xiong

  2. Mathematical Sciences Institute, Australian National University, Building 27, Canberra, ACT, 0200, Australia

    Changwei Xiong

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  1. Haizhong Li
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  2. Changwei Xiong
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Correspondence to Changwei Xiong.

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Li, H., Xiong, C. Stability of Capillary Hypersurfaces with Planar Boundaries. J Geom Anal 27, 79–94 (2017). https://doi.org/10.1007/s12220-015-9674-7

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  • DOI: https://doi.org/10.1007/s12220-015-9674-7

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