A Bernstein Type Theorem For Self-similar Shrinkers

Details A Bernstein Type Theorem For Self-similar Shrinkers A Bernstein Type Theorem For Self-similar Shrinkers

2009-12-09

arxiv.org/abs/0912.1809v1

Mathematics

Differential Geometry

7 pages

Scientific paper

In this note, we prove that smooth self-shrinkers in $\Real^{n+1}$, 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.

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