## Kähler-Einstein metrics on Fano manifolds. I: Approximation of metrics with cone singularities

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- by Xiuxiong Chen, Simon Donaldson and Song Sun
- J. Amer. Math. Soc.
**28**(2015), 183-197 - DOI: https://doi.org/10.1090/S0894-0347-2014-00799-2
- Published electronically: March 28, 2014
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## Abstract:

This is the first of a series of three papers which prove the fact that a*K*-stable Fano manifold admits a Kähler-Einstein metric. The main result of this paper is that a Kähler-Einstein metric with cone singularities along a divisor can be approximated by a sequence of smooth Kähler metrics with controlled geometry in the Gromov-Hausdorff sense.

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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: xiu@math.sunysb.edu
**Simon Donaldson**- Affiliation: Department of Mathematics, Imperial College London, London, U.K.
- Email: s.donaldson@imperial.ac.uk
**Song Sun**- Affiliation: Department of Mathematics, Imperial College London, London, U.K.
- MR Author ID: 879901
- Email: s.sun@imperial.ac.uk
- 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 2104 American Mathematical Society
- Journal: J. Amer. Math. Soc.
**28**(2015), 183-197 - MSC (2010): Primary 53C55
- DOI: https://doi.org/10.1090/S0894-0347-2014-00799-2
- MathSciNet review: 3264766