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

Departamento de Geometría y Topología, Instituto de Matemáticas (IEMath-GR), Universidad de Granada, 18071 Granada, Spain
Mathematics 2019, 7(12), 1211; https://doi.org/10.3390/math7121211
Received: 13 November 2019 / Revised: 3 December 2019 / Accepted: 5 December 2019 / Published: 9 December 2019
(This article belongs to the Special Issue Differential Geometry: Theory and Applications)
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. View Full-Text
Keywords: Euclidean space; Lorentz-Minkowski space; Dirichlet problem; mean curvature; maximum principle Euclidean space; Lorentz-Minkowski space; Dirichlet problem; mean curvature; maximum principle
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López, R. The Dirichlet Problem of the Constant Mean Curvature in Equation in Lorentz-Minkowski Space and in Euclidean Space. Mathematics 2019, 7, 1211.

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