On a Class of Fully Nonlinear Flow in K\"ahler Geometry

GEOMETRIC PDE SEMINAR
Topic:On a Class of Fully Nonlinear Flow in K\"ahler Geometry
Speaker:Hao Fang
Affiliation:The University of Iowa and Member, School of Mathematics
Date:Tuesday, March 31
Time/Room:2:00pm - 3:00pm/S-101

We study a class of fully nonlinear metric flow on K\"ahler manifolds, which includes the J-flow as a special case. We provide a sufficient and necessary condition for the long time convergence of the flow, generalizing the result of Song-Weinkove. As a consequence, under the given condition, we solved the corresponding Euler equation, which is fully nonlinear of Monge-Amp\`ere type. As an application, we also discuss a complex Monge-Amp\`ere type equation including terms of mixed degrees, which was first studied by Chen. This is a joint work with M. Lai and X. Ma.