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Durham e-Theses
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Maximal Graphs and Spacelike Mean Curvature Flows in Semi-Euclidean Spaces

THORPE, BENJAMIN,STUART (2011) Maximal Graphs and Spacelike Mean Curvature Flows in Semi-Euclidean Spaces. Doctoral thesis, Durham University.

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Two main results are proved. The first is for the maximal graph system in semi-Euclidean spaces. Existence of smooth solutions to the Dirichlet problem is proved, under certain assumptions on the boundary data. These assumptions allow the application of standard elliptic PDE methods by providing sufficiently strong a priori gradient estimates. The second result is a version of Brian White’s local regularity theorem, but now for the spacelike mean curvature flow system in semi-Euclidean spaces. This is proved using a version of Huisken’s monotonicity formula. Under the assumption of a suitable gradient bound, this theorem will give a priori estimates that allow such flows to be smoothly extended locally.

Item Type:Thesis (Doctoral)
Award:Doctor of Philosophy
Faculty and Department:Faculty of Science > Mathematical Sciences, Department of
Thesis Date:2011
Copyright:Copyright of this thesis is held by the author
Deposited On:11 Apr 2011 13:01

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