Communications in Analysis and Geometry
Volume 20 (2012)
The maximal graph Dirichlet problem in semi-Euclidean spaces
Pages: 255 – 270
The maximal graph Dirichlet problem asks whether thereexists a spacelike graph, in a semi-Euclidean space, with agiven boundary and with mean curvature everywhere zero. Weprove the existence of solutions to this problem undercertain assumptions on the given boundary. Mostimportantly, the results proved here will hold for graphsof codimension greater than $1$.