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.