Ricci flow on Orbifold

Abstract

In this paper, we study the behavior of Ricci flows on compact orbifolds with finite singularities. We show that Perelman's pseudolocality theorem also holds on orbifold Ricci flow. Using this property, we obtain a weak compactness theorem of Ricci flows on orbifolds under some natural technical conditions. This generalizes the corresponding theorem on manifolds. As an application, we can use Kähler Ricci flow to find new Kähler Einstein metrics on some orbifold Fano surfaces. For example, if $Y$ is a cubic surface with only one ordinary double point or $Y$ is an orbifold Fano surface with degree 1 and every singularity on it is a rational double point of type $\A_k (1 \leq k \leq 6)$, then we can find a KE metric of $Y$ by running Kähler Ricci flow.

References in corpus (14)

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Cited by in corpus (1)

• Kahler-Einstein metrics on Fano manifolds, III: limits as cone angle approaches 2π and completion of the main proof