The Moser-Trudinger inequality on Kahler-Einstein manifolds

摘要

We prove the conjecture of Tian on the strong form of the Moser-Trudingerinequality for Kahler-Einstein manifolds with positive first Chern class, whenthere are no holomorphic vector fields, and, more generally, when the settingis invariant under a maximal compact subgroup of the automorphism group.