As on arXiv
Abstract
We study mean convex mean curvature flow of local spacelike graphs in the flat slicing of de Sitter space. We show that if the initial slice is of non-negative time and is graphical over a large enough ball, and if is of bounded mean curvature, then as goes to infinity, becomes graphical in expanding balls, over which the gradient function converges to . In particular, if is the point lying over the center of the domain ball in , then converges smoothly to the flat slicing of de Sitter space. This has some relation to the mean curvature flow approach to the cosmic no hair conjecture.
Its neighbourhood
Connected papers
The 8 papers on this site closest to this one, judged by the topics they share, the words and phrases in their titles and abstracts, and their authors. They are not its citations, but a map of the work around it. Papers here go back to 2021, plus the canon.
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Soliton Solutions to the Curvature Flow on the 2-dimensional De Sitter Space and Applications
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Topics Physics, Long-time existence & convergence · Shared terms “Sitter space”, “converges smoothly”
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Topics Physics · Shared terms “Sitter space”, “spacelike”, “mean convex”
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Foliations by constant spacetime mean curvature surfaces for asymptotically hyperboloidal initial data sets
Topics Physics · Shared terms “Sitter”
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Volume preserving spacetime mean curvature flow and foliations of initial data sets
Topics Physics, Long-time existence & convergence
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Prescribed mean curvature flow for noncompact hypersurfaces in Lorentz manifolds
Topics Physics, Long-time existence & convergence · Shared terms “spacelike”
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In the guidebook
- 6A.10Curve Shortening and the First Geometric Flows
Shrinking circles, grim reapers, neckpinches and Huisken’s monotonicity, seen in the plane.