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Journal of the American Mathematical Society

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ISSN 1088-6834 (online) ISSN 0894-0347 (print)

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Kähler-Einstein metrics on Fano manifolds. III: Limits as cone angle approaches \boldmath$2\pi$ and completion of the main proof
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by Xiuxiong Chen, Simon Donaldson and Song Sun
J. Amer. Math. Soc. 28 (2015), 235-278
Published electronically: March 28, 2014


This is the third and final article in a series which prove the fact that a K-stable Fano manifold admits a Kähler-Einstein metric. In this paper we consider the Gromov-Hausdorff limits of metrics with cone singularities in the case when the limiting cone angle approaches 2$\pi$. We also put all our technical results together to complete the proof of the main theorem.
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Bibliographic Information
  • Xiuxiong Chen
  • Affiliation: Department of Mathematics, Stony Brook University, Stony Brook, New York 11794-3651 – and – School of Mathematics, University of Science and Technology of China, Hefei, Anhui, 230026, PR China
  • MR Author ID: 632654
  • Email:
  • Simon Donaldson
  • Affiliation: Department of Mathematics, Imperial College London, London, U.K.
  • Email:
  • Song Sun
  • Affiliation: Department of Mathematics, Imperial College London, London, U.K.
  • MR Author ID: 879901
  • Email:
  • Received by editor(s): March 8, 2013
  • Received by editor(s) in revised form: October 4, 2013, and January 13, 2014
  • Published electronically: March 28, 2014
  • Additional Notes: The first author was partly supported by National Science Foundation grant No 1211652; the last two authors were partly supported by the European Research Council award No 247331.
  • © Copyright 2014 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 28 (2015), 235-278
  • MSC (2010): Primary 53C55
  • DOI:
  • MathSciNet review: 3264768