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Complete Self‐Shrinking Solutions for Lagrangian Mean Curvature Flow in Pseudo‐Euclidean Space

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  • Ruiwei Xu
  • Linfen Cao

Abstract

Let f(x) be a smooth strictly convex solution of det(∂2f/∂xi∂xj)=exp(12/)∑i=1nxi(∂f/∂xi)-f defined on a domain Ω⊂Rn; then the graph M∇f of ∇f is a space‐like self‐shrinker of mean curvature flow in Pseudo‐Euclidean space Rn2n with the indefinite metric ∑dxidyi. In this paper, we prove a Bernstein theorem for complete self‐shrinkers. As a corollary, we obtain if the Lagrangian graph M∇f is complete in Rn2n and passes through the origin then it is flat.

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Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:196751
DOI: 10.1155/2014/196751
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