Convergence of a Kähler-Ricci flow

Abstract

In this paper we prove that for a given Kähler-Ricci flow with uniformly bounded Ricci curvatures in an arbitrary dimension, for every sequence of times $t_i$ converging to infinity, there exists a subsequence such that $(M,g(t_i+t))\to (Y,\bar{g}(t))$ and the convergence is smooth outside a singular set (which is a set of codimension at least 4) to a solution of a flow. We also prove that in the case of complex dimension 2, without any curvature assumptions we can find a subsequence of times such that we have a convergence to a Kähler-Ricci soliton, away from finitely many isolated singularities.

References in corpus (1)

• Gaussian densities and stability for some Ricci solitons

Cited by in corpus (1)

• The Kähler-Ricci flow on Kähler manifolds with 2 traceless bisectional curvature operator