A Bando-Mabuchi Uniqueness Theorem

TL;DR

This paper proves a uniqueness theorem for generalized Kahler-Einstein metrics on Fano manifolds, extending previous results by leveraging convexity of Bergman kernels and advanced regularization techniques.

Contribution

It generalizes Berndtsson's uniqueness theorem by applying new regularization methods and convexity properties to a broader class of Kahler-Einstein metrics.

Findings

Established a new uniqueness theorem for generalized Kahler-Einstein metrics.

Extended the scope of previous uniqueness results to more general Fano manifolds.

Utilized advanced regularization and convexity techniques in the proof.

Abstract

In this paper we prove a uniqueness theorem on generalized Kahler-Einstein metrics on Fano manifolds. Our result generalize the one shown by Berndtsson using the convexity properties of Bergman kernels. The same technics as well as that of the regularization of closed positive currents and an estimate due to Demailly-Kollar will be used in our proof.