The rigidity theorems for Lagrangian self shrinkers

Qi Ding; Y. L. Xin

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arXiv · 1112.2453

The rigidity theorems for Lagrangian self shrinkers

Qi Ding·Y. L. Xin

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Abstract

By the integral method we prove that any space-like entire graphic self-shrinking solution to Lagrangian mean curvature flow in $\R^{2n}_{n}$ with the indefinite metric $\sum_i dx_idy_i$ is flat. This result improves the previous ones in \cite{HW} and \cite{CCY} by removing the additional assumption in their results. In a similar manner, we reprove its Euclidean counterpart which is established in \cite{CCY}.

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Qi Ding, Y. L. Xin. 2011-12-12. The rigidity theorems for Lagrangian self shrinkers. https://arxiv.org/abs/1112.2453

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