The twisted Kahler-Ricci flow

TL;DR

This paper investigates a generalized Kahler-Ricci flow twisted by a non-negative form, proving exponential convergence to twisted Kahler-Einstein metrics when they exist, extending Perelman's results and building on Tian-Zhu's work.

Contribution

It introduces and analyzes a twisted version of the Kahler-Ricci flow, establishing convergence results that generalize previous findings.

Findings

Exponential convergence of the twisted flow when a twisted Kahler-Einstein metric exists

Extension of Perelman's convergence results to the twisted setting

Builds on Tian-Zhu's work to broaden understanding of Kahler-Ricci flows

Abstract

In this paper we study a generalization of the Kahler-Ricci flow, in which the Ricci form is twisted by a closed, non-negative (1,1)-form. We show that when a twisted Kahler-Einstein metric exists, then this twisted flow converges exponentially. This generalizes a result of Perelman on the convergence of the Kahler-Ricci flow, and it builds on work of Tian-Zhu.