Mean curvature flow in asymptotically flat product spacetimes
Mean curvature flow in asymptotically flat product spacetimes
Date
2021
Authors
Kröncke, Klaus
Lindblad Petersen, Oliver
Lubbe, Felix
Marxen, Tobias
Meiser, Wolfgang
Szabó, Áron
Vertman, Boris
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The Journal of Geometric Analysis ; 31 (2021). - pp. 5451-5479. - Springer. - ISSN 1050-6926. - eISSN 1559-002X
Abstract
We consider the long-time behaviour of the mean curvature flow of spacelike hypersurfaces in the Lorentzian product manifold M×R, where M is asymptotically flat. If the initial hypersurface F0⊂M×R is uniformly spacelike and asymptotic to M×{s} for some s∈R at infinity, we show that the mean curvature flow starting at F0 exists for all times and converges uniformly to M×{s} as t→∞.
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530 Physics
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mean curvature flow, asymptotically flat manifolds, static spacetimes
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KRÖNCKE, Klaus, Oliver LINDBLAD PETERSEN, Felix LUBBE, Tobias MARXEN, Wolfgang MAURER, Wolfgang MEISER, Oliver C. SCHNÜRER, Áron SZABÓ, Boris VERTMAN, 2021. Mean curvature flow in asymptotically flat product spacetimes. In: The Journal of Geometric Analysis. Springer. 31, pp. 5451-5479. ISSN 1050-6926. eISSN 1559-002X. Available under: doi: 10.1007/s12220-020-00486-zBibTex
@article{Kroncke2021curva-47071, year={2021}, doi={10.1007/s12220-020-00486-z}, title={Mean curvature flow in asymptotically flat product spacetimes}, volume={31}, issn={1050-6926}, journal={The Journal of Geometric Analysis}, pages={5451--5479}, author={Kröncke, Klaus and Lindblad Petersen, Oliver and Lubbe, Felix and Marxen, Tobias and Maurer, Wolfgang and Meiser, Wolfgang and Schnürer, Oliver C. and Szabó, Áron and Vertman, Boris} }
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