Bernstein theorem for translating solitons of hypersurfaces

Li Ma; M. Vicente

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arXiv · 1405.3042

Bernstein theorem for translating solitons of hypersurfaces

Li Ma·M. Vicente

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Abstract

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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Li Ma, M. Vicente. 2014-05-13. Bernstein theorem for translating solitons of hypersurfaces. https://arxiv.org/abs/1405.3042

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