The Maximal Graph Dirichlet Problem in Semi-Euclidean Spaces

Mathematics – Analysis of PDEs

Scientific paper

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Scientific paper

The maximal graph Dirichlet problem asks whether there exists a spacelike
graph, in a semi-Euclidean space, with a given boundary and with mean curvature
everywhere zero. We prove the existence of solutions to this problem under
certain assumptions on the given boundary. Most importantly, the results proved
here will hold for graphs of codimension greater than 1.

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