Liouville theorem of the subcritical biharmonic equation on complete manifolds
数学专题报告
报告题目(Title)：Liouville theorem of the subcritical biharmonic equation on complete manifolds
报告人(Speaker)：麻希南 教授 (中国科学技术大学)
地点(Place)：后主楼 1220
时间(Time)：2025 年 9 月 18 日（周四）下午 17：00-18：00
邀请人(Inviter)：周渊
报告摘要
We study the subcritical biharmonic equation
\[
\Delta^2 u = u^\alpha
\]
on a complete, connected, and non-compact Riemannian manifold \((M^n,g)\) with nonnegative Ricci curvature. By the vector field methods, under the assumption \(\Delta u \leq 0\) we derive a differential identity to obtain a Liouville theorem, i.e., there is no positive \(C^4\) solution if \(n \geq 5\) and \(1 < \alpha < \frac{n+4}{n-4}\). We establish a crucial second-order derivative estimate, which is established via Bernstein's technique and the continuity method.
This is the joint work with Tian Wu and Wangzhe Wu.
