Bernstein theorem for translating solitons of hypersurfaces

  • Li MaEmail author
  • Vicente Miquel


In this paper, we prove a monotonicity formula and some Bernstein type results for translating solitons of hypersurfaces in \(\mathbb {R}^{n+1}\), giving some conditions under which a translating 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.

Mathematics Subject Classification

53C21 53C44 


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The authors are very grateful to the unknown referees for helpful suggestions.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mathematics and PhysicsUniversity of Science and Technology BeijingBeijingPeople’s Republic of China
  2. 2.Department of MathematicsUniversity of ValenciaBurjassotSpain

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