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

2019/12/17 by López, Rafael
#53A10 #53C50 #58G20 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1912.07866

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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