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Mean curvature flow of entire graphs in a half-space with a free boundary

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Published/Copyright: May 3, 2012
Journal für die reine und angewandte Mathematik (Crelles Journal)
From the journal Journal für die reine und angewandte Mathematik (Crelles Journal) Volume 2014 Issue 690

Abstract.

We study the mean curvature flow of graphs with prescribed contact angle on a fixed, smooth hyperplane in Euclidean space. We obtain long time existence and convergence to a self similar solution of the mean curvature flow orthogonal to the fixed hyperplane.

The results from this paper are partially contained in the author's Ph.D. thesis [Mean curvature flow of graphs with free boundaries, Ph.D. thesis, Freie Universität Berlin, 2011], under the supervision of Prof. Dr. Klaus Ecker at the Freie Universität in Berlin, in the group of Geometric Analysis as a Berlin Mathematical School student. The author would like to thank them for financial support and help during the completion of this paper and her thesis.

Received: 2011-4-25
Revised: 2012-1-4
Published Online: 2012-5-3
Published in Print: 2014-5-1

© 2014 by Walter de Gruyter Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. UC hierarchy and monodromy preserving deformation
  3. Vector-valued p-adic Siegel modular forms
  4. K-theoretic Schubert calculus for OG(n,2n+1) and jeu de taquin for shifted increasing tableaux
  5. Strichartz estimates for partially periodic solutions to Schrödinger equations in 4d and applications
  6. Inverse tunneling estimates and applications to the study of spectral statistics of random operators on the real line
  7. Mean curvature flow of entire graphs in a half-space with a free boundary
  8. Ricci flow and the holonomy group
  9. Uniqueness of compact tangent flows in Mean Curvature Flow
  10. Even unimodular Lorentzian lattices and hyperbolic volume
  11. Algebraic points on Shimura curves of Γ0(p)-type
  12. Errata to Algebraic points on Shimura curves of Γ0(p)-type (J. reine angew. Math., DOI 10.1515/crelle-2012-0068)
  13. Property A and the operator norm localization property for discrete metric spaces
  14. Stable manifolds for holomorphic automorphisms
https://doi.org/10.1515/crelle-2012-0028

Articles in the same Issue

  1. Frontmatter
  2. UC hierarchy and monodromy preserving deformation
  3. Vector-valued p-adic Siegel modular forms
  4. K-theoretic Schubert calculus for OG(n,2n+1) and jeu de taquin for shifted increasing tableaux
  5. Strichartz estimates for partially periodic solutions to Schrödinger equations in 4d and applications
  6. Inverse tunneling estimates and applications to the study of spectral statistics of random operators on the real line
  7. Mean curvature flow of entire graphs in a half-space with a free boundary
  8. Ricci flow and the holonomy group
  9. Uniqueness of compact tangent flows in Mean Curvature Flow
  10. Even unimodular Lorentzian lattices and hyperbolic volume
  11. Algebraic points on Shimura curves of Γ0(p)-type
  12. Errata to Algebraic points on Shimura curves of Γ0(p)-type (J. reine angew. Math., DOI 10.1515/crelle-2012-0068)
  13. Property A and the operator norm localization property for discrete metric spaces
  14. Stable manifolds for holomorphic automorphisms
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