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

DOI10.1093/IMRN/RNX136zbMATH Open1462.53088arXiv1610.09285OpenAlexW2963053310MaRDI QIDQ5233828

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Publication date: 9 September 2019

Published in: (Search for Journal in Brave)

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.

Full work available at URL: https://arxiv.org/abs/1610.09285

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