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Transactions of the American Mathematical Society

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Collapsing of products along the Kähler-Ricci flow


Author: Matthew Gill
Journal: Trans. Amer. Math. Soc. 366 (2014), 3907-3924
MSC (2010): Primary 53C44; Secondary 53C55
DOI: https://doi.org/10.1090/S0002-9947-2013-06073-4
Published electronically: November 14, 2013
MathSciNet review: 3192623
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Abstract: Let $ X = M \times E$, where $ M$ is an $ m$-dimensional Kähler manifold with negative first Chern class and $ E$ is an $ n$-dimensional complex torus. We obtain $ C^\infty $ convergence of the normalized Kähler-Ricci flow on $ X$ to a Kähler-Einstein metric on $ M$. This strengthens a convergence result of Song-Weinkove and confirms their conjecture.


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Additional Information

Matthew Gill
Affiliation: Department of Mathematics, University of California, San Diego, 9500 Gilman Drive #0112, La Jolla, California 92093
Address at time of publication: Department of Mathematics, University of California, Berkeley, 970 Evans Hall #3840, Berkeley, California 94720-3840

DOI: https://doi.org/10.1090/S0002-9947-2013-06073-4
Received by editor(s): June 14, 2012
Received by editor(s) in revised form: December 17, 2012
Published electronically: November 14, 2013
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.