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
Stephen S-T. Yau
Speaker
Genglong 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.