Convergence of the Kähler–Ricci Flow on a Kähler–Einstein Fano Manifold
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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.
KeywordsCohomology Class Ricci Soliton Ricci Flow DelPezzo Surface Fano Variety
It is a pleasure to thank D.H.Phong for patiently explaining several aspects of the proof of this result.
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