The Dirichlet Problem of the Constant Mean Curvature in Equation in Lorentz-Minkowski Space and in Euclidean Space López Camino, Rafael Euclidean space Lorentz-Minkowski space Dirichlet problem Mean curvature Maximum principle 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. 2020-01-24T09:10:42Z 2020-01-24T09:10:42Z 2019-12-09 info:eu-repo/semantics/article López, R. (2019). The Dirichlet Problem of the Constant Mean Curvature in Equation in Lorentz-Minkowski Space and in Euclidean Space. Mathematics, 7(12), 1211. http://hdl.handle.net/10481/59106 10.3390/math7121211 eng http://creativecommons.org/licenses/by/3.0/es/ info:eu-repo/semantics/openAccess Atribución 3.0 España MDPI