Geometry & Topology

Notes on Perelman's papers

Bruce Kleiner and John Lott

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These are detailed notes on Perelman’s papers “The entropy formula for the Ricci flow and its geometric applications” [?] and “Ricci flow with surgery on three-manifolds” [?].

Article information

Geom. Topol., Volume 12, Number 5 (2008), 2587-2855.

Received: 22 February 2007
Revised: 19 September 2008
Accepted: 11 October 2008
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M40: Characterizations of $E^3$ and $S^3$ (Poincaré conjecture) [See also 57N12] 57M50: Geometric structures on low-dimensional manifolds
Secondary: 53C21: Methods of Riemannian geometry, including PDE methods; curvature restrictions [See also 58J60] 53C44: Geometric evolution equations (mean curvature flow, Ricci flow, etc.)

Perelman three-manifold geometrization theorem Poincaré Conjecture Ricci flow Ricci flow with surgery entropy formula long-term behaviour


Kleiner, Bruce; Lott, John. Notes on Perelman's papers. Geom. Topol. 12 (2008), no. 5, 2587--2855. doi:10.2140/gt.2008.12.2587.

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