The rigidity theorems for Lagrangian self shrinkers
Abstract
By the integral method we prove that any space-like entire graphic self-shrinking solution to Lagrangian mean curvature flow in 2nn with the indefinite metric Σi dxidyi is flat. This result improves the previous ones in HW and CCY by removing the additional assumption in their results. In a similar manner, we reprove its Euclidean counterpart which is established in CCY.
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