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. - 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.

Cite This

Files in this item

Files Size Format View

There are no files associated with this item.

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. 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

This item appears in the following Collection(s)

Search KOPS


Browse

My Account