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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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