A Bernstein Theorem for the Self-Shrinking J-Equation and Related Equations

报告人：王文龙（南开大学）

时  间：2026年6月5日10:00

地  点：海韵园实验楼S204

内容摘要:

In this talk, I will first review some established rigidity results for entire self-shrinking solutions arising from the Kähler-Ricci flow and mean curvature flow. I will then present a Bernstein theorem for the self-shrinking J-equation, showing that every entire smooth solution must be a quadratic polynomial. This removes the additional asymptotic lower bound assumption on the complex Hessian in a previous result of Xiaoli Han and Xishen Jin. I will also explain how our method applies to a broad class of fully nonlinear elliptic operators, including the inverse complex Hessian quotient operators. This is joint work with my master student Yiyang Pan.

个人简介：

王文龙，博士毕业于北京大学，现为南开大学副教授。研究方向是几何分析，特别是数量曲率相关问题，以及几何背景的完全非线性PDE。在Crelle, Math. Ann., CVPDE, IMRN等期刊上发表过论文。

联系人：桂耀挺