报告题目: New complex Hessian equations and their applications

报告人: 方浩 教授 (美国 Iowa大学)

时间: 2024年7月29日 (周一) 10:00-11:00

地点: 理科楼A304

摘要:   Fully non-linear Hessian equations have played fundamental roles in the study of complex geometry, following pioneering works of Yau. We discuss some new PDEs of similar fashion.

In a joint work with J. Jordan, we introduce a split type PDE on complex surfaces with split tangent and establish its solvability. As applications, we solve the corresponding prescribing Bismut-Ricci problem. Furthermore, we establish canonical metrics for Hopf surfaces and Inoue surfaces of type M, 2 important non-Kahler complex surfaces.

In a joint work with Biao Ma, we introduce a fully non-linear PDE with forms, generalizing J-equation and the dHYM equations. We give precise positive conditions under which general analytical and numerical criteria for the existence of smooth solutions can be established, generalizing works of G. Chen, J. Song and others. We also discuss applications to dHYM equations.

报告人简介：Professor Hao Fang is from University of Iowa. He earned his Bachelor degree in Nankai Univeristy and his PhD degree in Princeton University. His research interests include differential geometry and geometric analysis.

邀请人: 李海中, 马辉, 陈大广