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Translators of flows by powers of the Gauss curvature

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Abstract

A \(K^{\alpha}\)-translator is a surface in Euclidean space \({\mathbb {R}}^3\) that moves by translations in a spatial direction under the \(K^{\alpha}\)-flow, where K is the Gauss curvature and \(\alpha\) is a constant. We classify all \(K^{\alpha}\)-translators that are rotationally symmetric. In particular, we prove that for each \(\alpha\) there is a \(K^{\alpha}\)-translator intersecting orthogonally the rotation axis. We also describe all \(K^{\alpha}\)-translators invariant by a uniparametric group of helicoidal motions and the translators obtained by separation of variables.

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Acknowledgements

The second author (R. López) is a member of the Institute of Mathematics of the University of Granada. This work has been partially supported by the Projects I+D+i PID2020-117868GB-I00, A-FQM-139-UGR18 and P18-FR-4049.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Firat University, Elazig, 23200, Turkey

    Muhittin Evren Aydin

  2. Departamento de Geometría y Topología, Universidad de Granada, Granada, 18071, Spain

    Rafael López

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  1. Muhittin Evren Aydin
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  2. Rafael López
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Correspondence to Rafael López.

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Aydin, M.E., López, R. Translators of flows by powers of the Gauss curvature. Annali di Matematica 202, 235–251 (2023). https://doi.org/10.1007/s10231-022-01239-1

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  • DOI: https://doi.org/10.1007/s10231-022-01239-1

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