Communications in Analysis and Geometry

Volume 20 (2012)

Number 2

The maximal graph Dirichlet problem in semi-Euclidean spaces

Pages: 255 – 270

DOI: https://dx.doi.org/10.4310/CAG.2012.v20.n2.a2

Author

Benjamin Stuart Thorpe (Department of Mathematical Sciences, Durham University, United Kingdom)

Abstract

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 $1$.

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Published 8 June 2012