Journal of the European Mathematical Society

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Volume 18, Issue 8, 2016, pp. 1813–1854
DOI: 10.4171/JEMS/630

Published online: 2016-06-21

Ricci flow on quasiprojective manifolds II

John Lott[1] and Zhou Zhang[2]

(1) University of California, Berkeley, USA
(2) University of Sydney, Australia

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.

Keywords: Ricci flow, Kähler, quasiprojective

Lott John, Zhang Zhou: Ricci flow on quasiprojective manifolds II. J. Eur. Math. Soc. 18 (2016), 1813-1854. doi: 10.4171/JEMS/630