The Kähler-Ricci flow on Fano manifolds
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arXiv
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| Format: | Preprint |
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2012
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| _version_ | 1866916155881422848 |
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| author | Cao, Huai-Dong |
| author_facet | Cao, Huai-Dong |
| contents | In this lecture notes, we aim at giving an introduction to the Kähler-Ricci flow (KRF) on Fano manifolds. It covers some of the developments of the KRF in its first twenty years (1984-2003), especially an essentially self-contained exposition of Perelman's uniform estimates on the scalar curvature, the diameter, and the Ricci potential function for the normalized Kähler-Ricci flow (NKRF), including the monotonicity of Perelman's μ-entropy and κ-noncollapsing theorems for the Ricci flow on compact manifolds.
The Notes is based on a mini-course on KRF delivered at University of Toulouse III in February 2010, a talk on Perelman's uniform estimates for NKRF at Columbia University's Geometry and Analysis Seminar in Fall 2005, and several conference talks, including "Einstein Manifolds and Beyond" at CIRM (Marseille - Luminy, fall 2007), "Program on Extremal Kähler Metrics and Kähler-Ricci Flow" at the De Giorgi Center (Pisa, spring 2008), and "Analytic Aspects of Algebraic and Complex Geometry" at CIRM (Marseille - Luminy, spring 2011). |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1212_6227 |
| institution | arXiv |
| publishDate | 2012 |
| record_format | arxiv |
| spellingShingle | The Kähler-Ricci flow on Fano manifolds Cao, Huai-Dong Differential Geometry In this lecture notes, we aim at giving an introduction to the Kähler-Ricci flow (KRF) on Fano manifolds. It covers some of the developments of the KRF in its first twenty years (1984-2003), especially an essentially self-contained exposition of Perelman's uniform estimates on the scalar curvature, the diameter, and the Ricci potential function for the normalized Kähler-Ricci flow (NKRF), including the monotonicity of Perelman's μ-entropy and κ-noncollapsing theorems for the Ricci flow on compact manifolds. The Notes is based on a mini-course on KRF delivered at University of Toulouse III in February 2010, a talk on Perelman's uniform estimates for NKRF at Columbia University's Geometry and Analysis Seminar in Fall 2005, and several conference talks, including "Einstein Manifolds and Beyond" at CIRM (Marseille - Luminy, fall 2007), "Program on Extremal Kähler Metrics and Kähler-Ricci Flow" at the De Giorgi Center (Pisa, spring 2008), and "Analytic Aspects of Algebraic and Complex Geometry" at CIRM (Marseille - Luminy, spring 2011). |
| title | The Kähler-Ricci flow on Fano manifolds |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/1212.6227 |