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.

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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