Communications in Analysis and Geometry

Volume 30 (2022)

Number 7

Longtime existence of Kähler–Ricci flow and holomorphic sectional curvature

Pages: 1479 – 1509

DOI: https://dx.doi.org/10.4310/CAG.2022.v30.n7.a2

Authors

Shaochuang Huang (Yau Mathematical Sciences Center, Tsinghua University, Beijing, China; and International Center for Mathematics, Southern University of Science and Technology, Shenzhen, China)

Man-Chun Lee (Department of Mathematics, Northwestern University, Evanston, Illinois, U.S.A.; and Department of Mathematics, Chinese University of Hong Kong)

Luen-Fai Tam (Institute of Mathematical Sciences and Department of Mathematics, Chinese University of Hong Kong)

Freid Tong (Department of Mathematics, Columbia University, New York, N.Y., U.S.A.; and Center for Mathematical Sciences and Applications, Harvard University, Cambridge, Massachusetts, U.S.A.)

Abstract

In this work, we obtain some sufficient conditions for the longtime existence of the Kähler–Ricci flow solution. Using the existence results, we generalize a result by Wu–Yau on the existence of Kähler–Einstein metric on noncompact complex manifolds.

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The first-named author’s research was partially supported by the China Postdoctoral Science Foundation, grant #2017T100059.

The third-named author’s research was partially supported by the Hong Kong RGC General Research Fund, grant #CUHK 14301517.

Received 26 June 2018

Accepted 17 February 2020

Published 25 May 2023