Volume 25, issue 4 (2021)

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Kähler manifolds with almost nonnegative curvature

Man-Chun Lee and Luen-Fai Tam

Geometry & Topology 25 (2021) 1979–2015
Abstract

We construct local and global solutions to the Kähler–Ricci flow from a noncollapsed Kähler manifold with curvature bounded from below. Combining with the mollification technique of McLeod–Simon–Topping, we show that the Gromov–Hausdorff limit of a sequence of complete noncompact noncollapsed Kähler manifolds with orthogonal bisectional curvature and Ricci curvature bounded from below is homeomorphic to a complex manifold. We also use it to study the complex structure of complete Kähler manifolds with nonnegative orthogonal bisectional curvature, nonnegative Ricci curvature and maximal volume growth.

Keywords
Kahler manifolds, Kahler-Ricci flow existence, uniformization
Mathematical Subject Classification 2010
Primary: 32Q15
Secondary: 53C44
References
Publication
Received: 14 October 2019
Revised: 18 May 2020
Accepted: 19 June 2020
Published: 12 July 2021
Proposed: John Lott
Seconded: Gang Tian, Bruce Kleiner
Authors
Man-Chun Lee
Department of Mathematics,
Northwestern University
Evanston, IL
United States
Luen-Fai Tam
The Institute of Mathematical Sciences and Department of Mathematics
The Chinese University of Hong Kong
Shatin, Hong Kong
China