Year: 2010
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Wang, Bing
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1662376922