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→∞.
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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} }