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The one dimensional case of the singular minimal surfaces with density

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Abstract

Given \(\alpha ,\lambda \in \mathbb {R}\), a singular minimal surface with density vector \(\mathbf {v}\) is a surface \(\Sigma \) in Euclidean space whose mean curvature H satisfies \(2H(p)= \alpha \langle N(p),\mathbf {v}\rangle /\langle p,\mathbf {v}\rangle +2\lambda \), \(p\in \Sigma \), being N the Gauss map of \(\Sigma \). In this paper we classify the class of these surfaces that are invariant by a one-parameter group of translations.

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Acknowledgements

The author wishes to express his thanks to the referee for several helpful comments, specially concerning to the discussion of the portrait of phase plane.

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Authors and Affiliations

  1. Departamento de Geometría y Topología Instituto de Matemáticas (IEMath-GR), Universidad de Granada, 18071, Granada, Spain

    Rafael López

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  1. Rafael López
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Correspondence to Rafael López.

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Partially supported by MEC-FEDER Grant No. MTM2017-89677-P.

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López, R. The one dimensional case of the singular minimal surfaces with density. Geom Dedicata 200, 303–320 (2019). https://doi.org/10.1007/s10711-018-0372-z

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