A Bernstein type theorem for self-similar shrinkers
By Lu Wang. 2009
87 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/be630f8df4263468ac6d1dc70d36a2235baea0a6
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In Applied Mathematics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Uniqueness of Self-similar Shrinkers with Asymptotically Conical Ends (2011, methodology): “Also, in [47], we established a Bernstein type theorem for smooth entirely graphical self-shrinkers in R, which generalized a result of Ecker and Huisken [11].”
- Volume growth, eigenvalue and compactness for self-shrinkers (2011, unknown): “Then by [8], we know that M is a hyperplane, which is also obtained in [16].”
- Rigidity of entire self-shrinking solutions to curvature flows (2010, background): “Recently, it was shown in [10] that any entire graphic hypersurface solution to (2) must be flat, hence generalizing an earlier result in [4].”