Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The K\"ahler-Ricci flow on Fano manifolds   In this lecture notes, we aim at giving an introduction to the K\"ahler-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 K\"ahler-Ricci
flow (NKRF), including the monotonicity of Perelman's \mu-entropy and
\kappa-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 K\"ahler Metrics and
K\"ahler-Ricci Flow" at the De Giorgi Center (Pisa, spring 2008), and "Analytic
Aspects of Algebraic and Complex Geometry" at CIRM (Marseille - Luminy, spring
2011).

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The categories of this paper are: hep-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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The categories of this paper are: plasm-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: supr-con
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The categories of this paper are: astro-ph
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The categories of this paper are: q-fin
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The categories of this paper are: nlin
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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci
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The categories of this paper are: eess
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The categories of this paper are: comp-gas
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The categories of this paper are: chem-ph