Kahler-Ricci flow on blowups along submanifolds

TL;DR

This paper investigates the Kahler-Ricci flow on manifolds with divisors contracted to submanifolds, showing convergence to a homeomorphic base space with Holder continuous potentials.

Contribution

It demonstrates the convergence and regularity properties of the Kahler-Ricci flow in the context of blowups along submanifolds, extending understanding of geometric flow behavior.

Findings

Kahler potentials are Holder continuous.

Flow converges in Gromov-Hausdorff topology.

Limit space is homeomorphic to the original manifold.

Abstract

In this short note, we study the behavior of Kaher-Ricci flow on Kahler manifolds which contract divisors to smooth submanifolds. We show that the Kahler potentials are Holder continuous and the flow converges sequentially in Gromov-Hausdorff topology to a compact metric space which is homeomorphic to the base manifold.