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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

The Kähler-Ricci flow around complete bounded curvature Kähler metrics


Authors: Albert Chau and Man-Chun Lee
Journal: Trans. Amer. Math. Soc. 373 (2020), 3627-3647
DOI: https://doi.org/10.1090/tran/8015
Published electronically: February 21, 2020
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Abstract | References | Additional Information

Abstract: We produce complete bounded curvature solutions to the Kähler-Ricci flow with existence time estimates, assuming only that the initial data is a smooth Kähler metric uniformly equivalent to another complete bounded curvature Kähler metric. We obtain related flow results for nonsmooth as well as degenerate initial conditions. We also obtain a stability result for complex space forms under the flow.


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Additional Information

Albert Chau
Affiliation: Department of Mathematics, The University of British Columbia, Room 121, 1984 Mathematics Road, Vancouver, B.C., Canada V6T 1Z2
Email: chau@math.ubc.ca

Man-Chun Lee
Affiliation: Department of Mathematics, The University of British Columbia, Room 121, 1984 Mathematics Road, Vancouver, B.C., Canada V6T 1Z2
Address at time of publication: Department of Mathematics, Room 225, Northwestern University, 2033 Sheridan Road, Evanston, Illinois 60208
Email: mclee@math.northwestern.edu

DOI: https://doi.org/10.1090/tran/8015
Keywords: K\"ahler Ricci flow, complete non-compact K\"ahler manifolds.
Received by editor(s): May 30, 2019
Received by editor(s) in revised form: September 17, 2019
Published electronically: February 21, 2020
Additional Notes: The first author’s research was partially supported by NSERC grant no. #327637-06.
Article copyright: © Copyright 2020 American Mathematical Society