The Dirichlet problem of the constant mean curvature equation in Lorentz-Minkowski space and in Euclidean space

Rafael López

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arXiv · 1912.07866

The Dirichlet problem of the constant mean curvature equation in Lorentz-Minkowski space and in Euclidean space

Rafael López

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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 to drop the hypothesis on the mean convexity which is required in the Euclidean case.

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Rafael López. 2019-12-17. The Dirichlet problem of the constant mean curvature equation in Lorentz-Minkowski space and in Euclidean space. https://arxiv.org/abs/1912.07866

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