Trieste Summer School , june 2005 Ricci flow with surgery
نویسنده
چکیده
These notes provides some details on the lectures 2,3,4 on the Ricci flow with surgery. They are not complete and probably contains some inaccuracies. Interested readers can find most exhaustives explanations on the Perelman's papers in [KL]. The aim of these lecture is to give the classification and the description of 3-dimensional κ-solutions. Let κ > 0 and (M n , g(t)) a solution of the Ricci flow. M n is supposed oriented. definition 1.1. (M, g(t)) is a κ-solution if • g(t) is an ancient solution of the Ricci flow ∂ ∂t g(t) = −2Ric g(t) , −∞ < t ≤ 0. • for each t, g(t) is a complete, non flat metric of bounded curvature and non negative curvature operator. • for each t, g(t) is κ-noncollapsed on all scales, i.e. if |Rm(g(t))| ≤ 1 r 2 on B = B(p, t, r), then vol g(t) (B) r n ≥ κ
منابع مشابه
Kähler-Ricci flow on complete manifolds
This is a paper based on author’s lectures delivered at the 2005 Clay Mathematics Institute summer school at MSRI. It serves as an overview on the Kähler-Ricci flow over complete noncompact manifolds.
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