Bubbling of the prescribed Q-curvature curvature equation on 4-manifolds in the null case

讲座时间 Datetime: 

星期五, 2019/03/15 - 从 14:30 到 16:00

地点 Venue: 

海滨红楼6号楼1楼会议室

报告人 Speaker: 

张宏 副研究员

单位 Affiliation: 

中国科技技术大学

报告摘要 Abstract: 

Assume that $(M,g_0)$ is a closed 4-manifold with zero $Q$-curvature. Let $f_0$ be a non-constant smooth function with $\max f(x)=0$ and the negative average. For $\lambda>0$ suitably small, we consider a family of prescribed $Q$-curvature equations $P_{g_0}u=(f_0+\lambda)e^{4u}$. First, we show that the minimizer $u_\lambda$ of the prescribed $Q$-curvature equation exhibits bubbling phenomenon in a certain limit regime as $\lambda \to 0$. Then, we prove the analogous phenomenon occurs in the corresponding prescribed $Q$-curvature flow.