Geometriae Dedicata

, Volume 151, Issue 1, pp 297–303

A Bernstein type theorem for self-similar shrinkers

Original Paper

DOI: 10.1007/s10711-010-9535-2

Cite this article as:
Wang, L. Geom Dedicata (2011) 151: 297. doi:10.1007/s10711-010-9535-2

Abstract

In this paper, we prove that smooth self-shrinkers in \({\mathbb R^{n+1}}\), that are entire graphs, are hyperplanes. Previously, Ecker and Huisken showed that smooth self-shrinkers, that are entire graphs and have at most polynomial growth, are hyperplanes. The point of this paper is that no growth assumption at infinity is needed.

Keywords

Mean curvature flowSelf-shrinkers

Mathematics Subject Classification (2000)

53C4253C44

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Mathematics DepartmentMassachusetts Institute of TechnologyCambridgeUSA