Bessel Functions, Heat Kernel and the Conical Kähler-Ricci Flow

Abstract

Following Donaldson's oppenness theorem on deforming a conical Kähler-Einstein metric, we prove a parabolic Schauder-type estimate with respect to conical metrics. As a corollary, we show that the conical Kähler-Ricci Flow exists for short time. The key is to establish the relevant heat kernel estimates, where we use the Weber's formula on Bessel function of the second kind and Carslaw's heat kernel representation in \cite{Car}.

82 pages, 2 figures, comments are welcome

References in corpus (5)

• Kahler-Einstein metrics on Fano manifolds, III: limits as cone angle approaches 2π and completion of the main proof
• Kahler-Einstein metrics on Fano manifolds, II: limits with cone angle less than 2 π
• Conical Kahler-Einstein metric revisited
• Ricci Flow in Two Dimensions
• Canonical smoothing of compact Alexandrov surfaces via Ricci flow

Cited by in corpus (16)

• Ricci flow on surfaces with conic singularities
• KAWA lecture notes on the Kähler-Ricci flow
• Smooth approximations of the Conical Kahler-Ricci flows
• The conical Kähler-Ricci flow on Fano manifolds
• On the long time behaviour of the Conical Kähler- Ricci flows
• The Ricci flow on the sphere with marked points
• Schauder estimates for equations with cone metrics, I
• Unnormalize conical Kähler-Ricci flow
• Ricci flow from spaces with isolated conical singularities
• On the regularity problem of complex Monge-Ampere equations with conical singularities
• $C^{2,\alpha }$-estimate for conical Kähler-Ricci flow
• 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
• Smooth approximation of the modified conical Kähler-Ricci flow
• On a twisted conical Kähler-Ricci flow
• Smoothing conic Kähler metrics with uniformly upper bisectional curvature bound