Mean curvature flow in asymptotically flat product spacetimes

Type of Publication: Journal article
Publication status: Published
Author: Kröncke, Klaus; Lindblad Petersen, Oliver; Lubbe, Felix; Marxen, Tobias; Maurer, Wolfgang; Meiser, Wolfgang; Schnürer, Oliver C.; Szabó, Áron; Vertman, Boris
Year of publication: 2020
Published in: The Journal of Geometric Analysis ; 2020. - Springer. - ISSN 1050-6926. - eISSN 1559-002X
ArXiv-ID: arXiv:1903.03502
DOI (citable link): https://dx.doi.org/10.1007/s12220-020-00486-z
Summary:
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→∞.
MSC Classification: 53C44; 53C50; 58J35
Subject (DDC): 530 Physics
Keywords: mean curvature flow, asymptotically flat manifolds, static spacetimes
Bibliography of Konstanz: Yes
Refereed: Unknown
Online First: Journal articles that are published online before they appear as an actual part of a journal issue. Online first articles are published on the journal's website in the publisher's version.

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KRÖNCKE, Klaus, Oliver LINDBLAD PETERSEN, Felix LUBBE, Tobias MARXEN, Wolfgang MAURER, Wolfgang MEISER, Oliver C. SCHNÜRER, Áron SZABÓ, Boris VERTMAN, 2020. Mean curvature flow in asymptotically flat product spacetimes. In: The Journal of Geometric Analysis. Springer. ISSN 1050-6926. eISSN 1559-002X. Available under: doi: 10.1007/s12220-020-00486-z

@article{Kroncke2020curva-47071, title={Mean curvature flow in asymptotically flat product spacetimes}, year={2020}, doi={10.1007/s12220-020-00486-z}, issn={1050-6926}, journal={The Journal of Geometric Analysis}, 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} }

Lubbe, Felix Meiser, Wolfgang Schnürer, Oliver C. 2019-09-27T12:56:27Z Kröncke, Klaus Marxen, Tobias Maurer, Wolfgang 2020 Vertman, Boris Lubbe, Felix Marxen, Tobias eng Kröncke, Klaus Szabó, Áron Szabó, Áron Mean curvature flow in asymptotically flat product spacetimes 2019-09-27T12:56:27Z 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 F<sub>0</sub>⊂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 F<sub>0</sub> exists for all times and converges uniformly to M×{s} as t→∞. Lindblad Petersen, Oliver Vertman, Boris Meiser, Wolfgang Schnürer, Oliver C. Maurer, Wolfgang Lindblad Petersen, Oliver

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