Asymptotic stability for Kähler-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 Kähler-Ricci soliton modulo automorphisms. In our results, we do not assume that the vanishing of the higher order modified Futaki invariants introduced by Berman-Nyström.

15 pages, final version, to appear in Mathematische Zeitschrift

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