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arXiv · 1610.09285

Rigidity of Entire Convex Self-Shrinking Solutions to Hessian Quotient Flows

Wenlong Wang
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Abstract

We prove that all entire smooth strictly convex self-shrinking solutions on $\mathbb{R}^n$ to the Hessian quotient flows must be quadratic. This generalizes the rigidity theorem for entire self-shrinking solutions to the Lagrangian mean curvature flow in pseudo-Euclidean space due to Ding-Xin \cite{DX}. Moreover, we show that our argument works for a larger class of equations. In particular, we obtain rigidity results for entire self-shrinking solutions on $\mathbb{C}^n$ to the K\"{a}hler-Ricci flow under certain conditions.

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Wenlong Wang. 2016-10-28. Rigidity of Entire Convex Self-Shrinking Solutions to Hessian Quotient Flows. https://arxiv.org/abs/1610.09285

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