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A regularity theorem
for graphic spacelike mean curvature flows
Benjamin Stuart Thorpe |
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Vol. 255 (2012), No. 2, 463–487
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Abstract |
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For mean curvature flows in Euclidean spaces, Brian White proved a regularity theorem which gives C2,α estimates in regions of spacetime where the Gaussian density is close enough to 1. This is proved by applying Huisken’s monotonicity formula. Here we will consider mean curvature flows in semi-Euclidean spaces, where each spatial slice is an m-dimensional graph in ℝnm+n satisfying a gradient bound stronger than the spacelike condition. By defining a suitable quantity to replace the Gaussian density ratio, we prove monotonicity theorems similar to Huisken’s and use them to prove a regularity theorem similar to White’s. |
Keywords
mean curvature flow, semi-Riemannian geometry
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Mathematical Subject Classification 2010
Primary: 35B65, 35K93
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Milestones
Received: 19 March 2011
Revised: 11 July 2011
Accepted: 17 October 2011
Published: 10 April 2012
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Authors |
| Benjamin Stuart Thorpe | |
| Department of Mathematical
Sciences Durham University Science Laboratories South Road Durham, DH1 3LE United Kingdom |
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