arxiv: 1405.3042 · v3 · pith:IQKNFWPOnew · submitted 2014-05-13 · 🧮 math.DG · math.AP

Bernstein theorem for translating solitons of hypersurfaces

Li Ma , M.Vicente This is my paper

classification 🧮 math.DG math.AP

keywords hypersurfacessolitontranslatingbernsteinhyperplanesolitonssometheorem

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In this paper, we prove a monotonicity formula and some Bernstein type results for translating solitons of hypersurfaces in $\re^{n+1}$, giving some conditions under which a trantranslating soliton is a hyperplane. We also show a gap theorem for the translating soliton of hypersurfaces in $R^{n+k}$, namely, if the $L^n$ norm of the second fundamental form of the soliton is small enough, then it is a hyperplane.

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Bernstein theorem for translating solitons of hypersurfaces

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