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Surfaces of constant anisotropic mean curvature with free boundary in revolution surfaces

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Abstract

In this paper we consider immersions with constant anisotropic mean curvature (CAMC) of a smooth oriented connected and compact surface \(\varSigma \), with non-empty boundary \(\partial \varSigma \), in a region \(\varOmega \) such that the boundary \(\partial \varOmega \) is a rotational surface. We prove that, under a suitable condition on the anisotropic function, the flat disks are the only free boundary CAMC immersions in \(\varOmega \). Moreover, we study which disks are stable. Finally, we consider an interesting result that allows us to build a wide variety of examples of Wulff Shape.

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Authors and Affiliations

  1. Departamento de Matemática, Universidade Federal de Minas Gerais (UFMG), Belo Horizonte, MG, Brazil

    Ezequiel Barbosa

  2. Instituto de Ciências, Exatas e Tecnológicas, Universidade Federal de Viçosa, Campus UFV Florestal, Florestal, MG, Brazil

    Lucas Carvalho Silva

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  1. Ezequiel Barbosa
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  2. Lucas Carvalho Silva
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Barbosa, E., Carvalho Silva, L. Surfaces of constant anisotropic mean curvature with free boundary in revolution surfaces. manuscripta math. 169, 439–459 (2022). https://doi.org/10.1007/s00229-021-01336-0

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