Ricci flow on quasiprojective manifolds II

Abstract

We study the Ricci flow on complete Kähler metrics that live on the complement of a divisor in a compact complex manifold. In earlier work, we considered finite-volume metrics which, at spatial infinity, are transversely hyperbolic. In the present paper we consider three different types of spatial asymptotics: cylindrical, bulging and conical. We show that in each case, the asymptotics are preserved by the Kähler–Ricci flow.We address long-time existence, parabolic blowdown limits and the role of the Kähler–Ricci flow on the divisor.