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.
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Wang, L. A Bernstein type theorem for self-similar shrinkers. Geom Dedicata 151, 297–303 (2011). https://doi.org/10.1007/s10711-010-9535-2
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DOI: https://doi.org/10.1007/s10711-010-9535-2