Uniqueness of compact tangent flows in Mean Curvature Flow
Abstract.
We show, for mean curvature flows in Euclidean space, that if one of
the tangent flows at a given space-time point consists of a closed,
multiplicity-one, smoothly embedded self-similar shrinker,
then it is the unique tangent flow at that point.
That is the limit of the parabolic rescalings does not depend on the
chosen sequence of rescalings. Furthermore, given such a
closed, multiplicity-one, smoothly embedded self-similar shrinker
Σ, we show that any solution of the rescaled flow, which is
sufficiently close to Σ, with Gaussian density ratios greater
or equal to that of Σ, stays for all time close
to Σ and converges to a possibly different self-similarly
shrinking solution
Funding source: Alexander von Humboldt Foundation
Award Identifier / Grant number: Feodor–Lynen fellowship
The author would like to thank K. Ecker, L. Simon, N. Wickramasekera, J. Bernstein and B. White for discussions and helpful comments on this paper. He would also like to thank the Department of Mathematics at Stanford University for their hospitality during the winter/spring of 2008 while the main part of this work was completed.
© 2014 by Walter de Gruyter Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- UC hierarchy and monodromy preserving deformation
- Vector-valued p-adic Siegel modular forms
- K-theoretic Schubert calculus for OG(n,2n+1) and jeu de taquin for shifted increasing tableaux
-
Strichartz estimates for partially periodic solutions to Schrödinger equations in
- Inverse tunneling estimates and applications to the study of spectral statistics of random operators on the real line
- Mean curvature flow of entire graphs in a half-space with a free boundary
- Ricci flow and the holonomy group
- Uniqueness of compact tangent flows in Mean Curvature Flow
- Even unimodular Lorentzian lattices and hyperbolic volume
- Algebraic points on Shimura curves of Γ0(p)-type
- Errata to Algebraic points on Shimura curves of Γ0(p)-type (J. reine angew. Math., DOI 10.1515/crelle-2012-0068)
- Property A and the operator norm localization property for discrete metric spaces
- Stable manifolds for holomorphic automorphisms
Artikel in diesem Heft
- Frontmatter
- UC hierarchy and monodromy preserving deformation
- Vector-valued p-adic Siegel modular forms
- K-theoretic Schubert calculus for OG(n,2n+1) and jeu de taquin for shifted increasing tableaux
-
Strichartz estimates for partially periodic solutions to Schrödinger equations in
- Inverse tunneling estimates and applications to the study of spectral statistics of random operators on the real line
- Mean curvature flow of entire graphs in a half-space with a free boundary
- Ricci flow and the holonomy group
- Uniqueness of compact tangent flows in Mean Curvature Flow
- Even unimodular Lorentzian lattices and hyperbolic volume
- Algebraic points on Shimura curves of Γ0(p)-type
- Errata to Algebraic points on Shimura curves of Γ0(p)-type (J. reine angew. Math., DOI 10.1515/crelle-2012-0068)
- Property A and the operator norm localization property for discrete metric spaces
- Stable manifolds for holomorphic automorphisms
