The Dirichlet Problem of the Constant Mean Curvature in Equation in Lorentz-Minkowski Space and in Euclidean Space

Rafael López
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Rafael López: Departamento de Geometría y Topología, Instituto de Matemáticas (IEMath-GR), Universidad de Granada, 18071 Granada, Spain

Mathematics, 2019, vol. 7, issue 12, 1-20

Abstract: We investigate the differences and similarities of the Dirichlet problem of the mean curvature equation in the Euclidean space and in the Lorentz-Minkowski space. Although the solvability of the Dirichlet problem follows standards techniques of elliptic equations, we focus in showing how the spacelike condition in the Lorentz-Minkowski space allows dropping the hypothesis on the mean convexity, which is required in the Euclidean case.

Keywords: Euclidean space; Lorentz-Minkowski space; Dirichlet problem; mean curvature; maximum principle (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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