Asymptotic stability for K\"ahler-Ricci solitons

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.

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