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Convergence of the Kähler–Ricci Flow on a Kähler–Einstein Fano Manifold

  • Vincent GuedjEmail author
Chapter
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Part of the Lecture Notes in Mathematics book series (LNM, volume 2086)

Abstract

The goal of these notes is to sketch the proof of the following result, due to Perelman and Tian–Zhu: on a Kähler–Einstein Fano manifold with discrete automorphism group, the normalized Kähler–Ricci flow converges smoothly to the unique Kähler–Einstein metric. We also explain an alternative approach due to Berman–Boucksom–Eyssidieux–Guedj–Zeriahi, which only yields weak convergence but also applies to Fano varieties with log terminal singularities.

Keywords

Cohomology Class Ricci Soliton Ricci Flow DelPezzo Surface Fano Variety 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

It is a pleasure to thank D.H.Phong for patiently explaining several aspects of the proof of this result.

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Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  1. 1.Institut de Mathématiques de Toulouse and Institut Universitaire de FranceUniversité Paul SabatierToulouse Cedex 9France

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