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Rotational Ricci surfaces

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Abstract

We classify rotational surfaces in the three-dimensional Euclidean space whose Gaussian curvature K satisfies

$$\begin{aligned} K\Delta K - \Vert \nabla K\Vert ^2-4K^3 = 0. \end{aligned}$$

These surfaces are referred to as rotational Ricci surfaces. As an application, we show that there is a one-parameter family of such surfaces meeting the boundary of the unit Euclidean three-ball orthogonally. In addition, we show that this family interpolates a vertical geodesic and the critical catenoid.

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Authors and Affiliations

  1. Department of Mathematics, KU Leuven, Celestijnenlaan 200B, Box 2400, 3001, Leuven, Belgium

    Iury Domingos

  2. Departamento de Matemática, Universidade Federal do Ceará, Campus do Pici, Av. Humberto Monte, Fortaleza, CE, 60455-760, Brazil

    Roney Santos

  3. Instituto de Matemática, Universidade Federal de Alagoas, Campus A. C. Simões, BR 104 - Norte, Km 97, Maceió, AL, 57072-970, Brazil

    Feliciano Vitório

Authors
  1. Iury Domingos
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  2. Roney Santos
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  3. Feliciano Vitório
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Correspondence to Iury Domingos.

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I. Domingos was supported by the Research Foundation-Flanders (FWO) and the Fonds de la Recherche Scientifique (FNRS) under EOS Project G0H4518N. R. Santos was supported by Instituto Serrapilheira, grant “New perspectives of the min-max theory for the area functional”. F. Vitório was partially supported by CNPq (405468/2021-0).

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Domingos, I., Santos, R. & Vitório, F. Rotational Ricci surfaces. Annali di Matematica (2024). https://doi.org/10.1007/s10231-024-01436-0

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  • DOI: https://doi.org/10.1007/s10231-024-01436-0

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