Kahler-Einstein metrics on Fano manifolds, III: limits as cone angle approaches 2\pi\ and completion of the main proof

By Xiuxiong Chen, Simon Donaldson, Song Sun. 2013

391 citations recorded by the source corpus.

This is the third and final paper in a series which establish results announced in arXiv:1210.7494. 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 that if a K-stable Fano manifold admits a Kahler-Einstein metric.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/870b3bce0463db423af52d2170c0646e5e884e0c

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In Applied Mathematics

1. R. Dervan
2. G'abor Sz'ekelyhidi
3. Chi Li
4. Song Sun
5. Robert J. Berman
6. Y. Odaka
7. Simon Donaldson
8. G. Tian

In Geometry and Topology

1. R. Dervan
2. G'abor Sz'ekelyhidi
3. Chi Li
4. Song Sun
5. Robert J. Berman
6. Y. Odaka
7. G. Tian
8. Simon Donaldson

Citations in the corpus

• The partial $C^0$-estimate along the continuity method (2013, methodology): “Following Chen-Donaldson-Sun [13] we introduce the invariant (9) I(Ω) = inf B(x,r)⊂Ω V R(x, r)”