Rigidity of entire self-shrinking solutions to Kähler-Ricci flow with strictly real convex potential

Abstract

We prove that every entire self-shrinking solution on ${\mathbb{C}}^n$ to the Kähler-Ricci flow with strictly real convex potential must be quadratic. The very same argument also gives a pointwise proof for the rigidity of entire self-shrinking solutions to Lagrangian mean curvature flow in pseudo-Euclidean space obtained by Q. Ding and Y.L. Xin. Furthermore, we show that our argument works for a larger class of equations.

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References in corpus (1)

• Entire self-similar solutions to Lagrangian Mean curvature flow