JournalsjemsVol. 18, No. 8pp. 1813–1854

Ricci flow on quasiprojective manifolds II

  • John Lott

    University of California, Berkeley, USA
  • Zhou Zhang

    University of Sydney, Australia
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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.

Cite this article

John Lott, Zhou Zhang, Ricci flow on quasiprojective manifolds II. J. Eur. Math. Soc. 18 (2016), no. 8, pp. 1813–1854

DOI 10.4171/JEMS/630