English

A Bernstein Type Theorem For Self-similar Shrinkers

Differential Geometry 2009-12-10 v1 Analysis of PDEs

Abstract

In this note, we prove that smooth self-shrinkers in \Realn+1\Real^{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 note is that no growth assumption at infinity is needed.

Keywords

Cite

@article{arxiv.0912.1809,
  title  = {A Bernstein Type Theorem For Self-similar Shrinkers},
  author = {Lu Wang},
  journal= {arXiv preprint arXiv:0912.1809},
  year   = {2009}
}

Comments

7 pages

R2 v1 2026-06-21T14:21:48.889Z