Notes on Perelman's papers

By Bruce Kleiner, J. Lott. 2006

630 citations recorded by the source corpus.

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".

Subfields: Applied Mathematics, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/d8c12651ad0a285e793b0f7c49cdc900e77f533c

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In Applied Mathematics

1. B. Weinkove
2. G'abor Sz'ekelyhidi
3. Jian Song
4. Valentino Tosatti
5. Duong H. Phong
6. G. Tian
7. Robert J. Berman
8. Jacob Sturm

In Mathematical Physics

1. Duong H. Phong
2. B. Leeb
3. J. Porti
4. B. Weinkove
5. Michael Kapovich
6. Reto Müller
7. Reto Muller
8. Xiang-Dong Li

In Statistical and Nonlinear Physics

1. Reto Müller
2. Reto Muller
3. Xiang-Dong Li
4. G. Tian
5. Bing Wang
6. Huiling Gu
7. Xiaohua Zhu
8. Xiping Zhu

Citations in the corpus

• Width and finite extinction time of Ricci flow (2007, neutral): “and Lott [18].”
• On the global well-posedness of energy-critical Schr\"odinger equations in curved spaces (2010, background): “The proof of Thurston’s conjecture can be found in [Cao and Zhu 2006; Kleiner and Lott 2008; Morgan and Tian 2007; Perelman 2002].”
• The Existence of Type II Singularities for the Ricci Flow on $S^{n+1}$ (2007, methodology): “Then exactly as Perelman’s argument in Theorem 12.1 of [27] (see also [ 26 ] and [10] for details), we can get that the curvature of the limit g∞(� ,t) at t = 0 has bounded curvature and also that the limit g∞(� ,t) can be defined on (−∞,0].”
• On a classification of the gradient shrinking solitons (2007, background): “ KL , MT] (see also pages 377-386 of [CLN]), is geometric and relies on detailed analysis of the level sets of the potential function, and more importantly, the Gauss-Bonnet formula for surfaces.”
• Convergence of Kähler-Ricci flow (2007, methodology): “Then by using the noncollapsing result of Ricci flow ([P1], [KL]) together with (A.”
• The Geometry and Topology of Coxeter Groups (2025, background): “(Also, see [49, 179, 219] for expositions of Perelman’s work.”
• On the Conditions to Extend Ricci Flow (2007, background): “We refer the readers to [11], [12] for more information.”
• Ricci flow coupled with harmonic map flow (2009, methodology): “Since the proof is very similar to the Ricci flow case solved by Perelman in [31], we closely follow the notes from Kleiner and Lott [19] on Perelman’s paper.”