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

Speaker：Wenlong Wang (Nankai University)

Time：2026-6-5 10:00

Location：Conference Room S204 at Experiment Building at Haiyun Campus

Abstract:

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.