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ENTIRE DOWNWARD TRANSLATING SOLITONS TO THE MEAN CURVATURE FLOW IN MINKOWSKI SPACE.
- Source :
- Proceedings of the American Mathematical Society; Aug2016, Vol. 144 Issue 8, p3517-3526, 10p
- Publication Year :
- 2016
-
Abstract
- In this paper, we study entire translating solutions u(x) to a mean curvature flow equation in Minkowski space. We show that if Σ = {(x, u(x))∣x ϵ R<superscript>n</superscript>} is a strictly spacelike hypersurface, then Σ reduces to a strictly convex rank k soliton in R<superscript>k,1</superscript> (after splitting off trivial factors) whose "blowdown" converges to a multiple λ ϵ (0, 1) of a positively homogeneous degree one convex function in R<superscript>k</superscript>. We also show that there is nonuniqueness as the rotationally symmetric solution may be perturbed to a solution by an arbitrary smooth order one perturbation. [ABSTRACT FROM AUTHOR]
- Subjects :
- SOLITONS
MINKOWSKI space
HYPERSURFACES
CONVEX functions
PERTURBATION theory
Subjects
Details
- Language :
- English
- ISSN :
- 00029939
- Volume :
- 144
- Issue :
- 8
- Database :
- Complementary Index
- Journal :
- Proceedings of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 115642445
- Full Text :
- https://doi.org/10.1090/proc/12969