Asymptotic stability for K\"ahler-Ricci solitons

TL;DR

This paper demonstrates that coercivity of the modified Ding functional guarantees the existence and convergence of balanced metrics to Kähler-Ricci solitons without assuming vanishing higher order invariants.

Contribution

It establishes a new link between the coercivity of the modified Ding functional and the existence of Kähler-Ricci solitons, removing previous assumptions about higher order invariants.

Findings

Balanced metrics converge to Kähler-Ricci solitons

No need for vanishing higher order Futaki invariants

Provides a new approach to stability and existence results

Abstract

We show that the coercivity of the modified Ding functional leads to the existence of a certain kind of balanced metrics and their convergence to the K\"ahler-Ricci soliton modulo automorphisms. In our results, we do not assume that the vanishing of the higher order modified Futaki invariants introduced by Berman-Nystr\"om.