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 (13)

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• Degeneration of Kähler-Ricci solitons
• Ricci flow on Orbifold
• The Sasaki-Ricci flow and compact Sasakian manifolds of positive transverse holomorphic bisectional curvature
• Convergence of Kaehler-Ricci flow with integral curvature bound
• Stability on Kähler-Ricci flow, I
• The Kähler-Ricci flow on Kähler manifolds with 2 traceless bisectional curvature operator
• The (logarithmic) Sobolev inequalities along geometric flow and applications
• Isoperimetric inequality under Kähler Ricci flow