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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Collapsing of products along the Kähler-Ricci flow
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by Matthew Gill PDF
Trans. Amer. Math. Soc. 366 (2014), 3907-3924 Request permission


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
  • MR Author ID: 951451
  • Received by editor(s): June 14, 2012
  • Received by editor(s) in revised form: December 17, 2012
  • Published electronically: November 14, 2013
  • © Copyright 2013 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 366 (2014), 3907-3924
  • MSC (2010): Primary 53C44; Secondary 53C55
  • DOI:
  • MathSciNet review: 3192623