Kähler–Ricci flow on blowups along submanifolds

Abstract

In this short note, we study the behavior of Kahler–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.