Smooth approximations of the Conical Kahler-Ricci flows

Abstract

In this note, we show that the conical Kähler-Ricci flows introduced in \cite{CYW} exist for all time $t\in [0,\infty )$ in the weak sense. As a key ingredient of the proof, we show that a conical Kähler-Ricci flow is actually the limit of a sequence of smooth Kähler-Ricci flows.

Reference updated especially on Bahuaud-Vertman's work on Yamabe flow, Mathematische Annalen. First online: 01 August 2015

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Cited by in corpus (13)

• The conical Kähler-Ricci flow on Fano manifolds
• On the long time behaviour of the Conical Kähler- Ricci flows
• Unnormalize conical Kähler-Ricci flow
• Ricci de Turck flow on singular manifolds
• On the regularity problem of complex Monge-Ampere equations with conical singularities
• $C^{2,\alpha }$-estimate for conical Kähler-Ricci flow
• Stability of Ricci de Turck flow on Singular Spaces
• The conical Kähler-Ricci flow with weak initial data on Fano manifold
• $C^{2,\alpha }$-estimate for Monge-Ampere equations with Hölder-continuous right hand side
• Smoothing conic Kähler metrics with uniformly upper bisectional curvature bound
• Remarks on the Hölder-continuity of solutions to parabolic equations with conic singularities
• Bounded Ricci Curvature and Positive Scalar Curvature under Singular Ricci de Turck Flow
• Stability of the conical Kähler-Ricci flows on Fano manifolds