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A Jenkins-Serrin theorem in M 2 × ℝ

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Abstract

In this paper we study minimal surfaces in M × ℝ, where M is a complete surface. Our main result is a Jenkins-Serrin type theorem which establishes necessary and sufficient conditions for the existence of certain minimal vertical graphs in M × ℝ. We also prove that there exists a unique solution of the Plateau’s problem in M × ℝ whoseboundaryisaNitschegraphandweconstructaScherk-typesurfaceinthisspace.

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Authors and Affiliations

  1. Departamento de Matemática, Universidade Federal da Bahia, Av. Ademar de Barros s/n, 40170-110, Salvador, BA, Brasil

    Ana Lucia Pinheiro

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  1. Ana Lucia Pinheiro
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Correspondence to Ana Lucia Pinheiro.

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Thanks to CNPq Agency for financial support.

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Pinheiro, A.L. A Jenkins-Serrin theorem in M 2 × ℝ. Bull Braz Math Soc, New Series 40, 117–148 (2009). https://doi.org/10.1007/s00574-009-0007-y

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  • DOI: https://doi.org/10.1007/s00574-009-0007-y

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