BIMSA > Seminar on Algebraic, Complex Geometry and Singularities Degenerate Hessian type equations on compact complex manifolds.
Degenerate Hessian type equations on compact complex manifolds.
Organizer
Shing Toung Yau
Speaker
Geng Long Lin
Time
Friday, August 23, 2024 10:30 AM - 11:30 AM
Venue
清华大学理科楼 A304
Abstract
Degenerate Monge-Ampere/Hessian equations play an important role in recent Differential Geometry and Complex Algebraic Geometry. In this talk we will review recent progress on Monge-Ampere equation and talk about a class of degenerate Monge-Ampere equations. As an application, we give an generalization on a solution of Dinew-Guedj-Zeriahi's conjecture due to Darvas-Di Nezza-Lu. Secondly, we will give an characterization of finite energy range of Hessian operator, which generalized the Monge-Ampere ones proved by Darvas-Di Nezza-Lu. The talk is based on my work and the joint work with Yinji Li and Prof. Xiangyu Zhou.