A thermodynamical formalism for Kahler-Einstein metrics on log Fano manifolds and applications
主 题: A thermodynamical formalism for Kahler-Einstein metrics on log Fano manifolds and applications
报告人: Prof. Robert Berman (Chalmers University, Sweden)
时 间: 2011-04-21 14:00-16:00
地 点: Room 1328 at BICMR, Resource Plaza
In this talk I will start by setting up a variational approach to rather general complex Monge-Ampère equations on a K?hler manifold X. The leading role
wil be played by a certain "free energy functional", which generalizes Mabuchi's K-energy functional. Applications to K?hler-Einstein metrics on log Fano manifolds will then be given. In particular, inspired by a recent program of Donaldson in the context of the the Yau-Tian-Donaldson conjecture, it will be explained how to obtain K?hler-Einstein metrics on a Fano manifold which are singular along a given Calabi-Yau hyper surface.