A Complete Proof of the Poincaré and Geometrization Conjectures - application of the Hamilton-Perelman theory of the Ricci flow

By Huaihuo Cao, Xiping Zhu. 2006

429 citations recorded by the source corpus.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/ff64ca93dbcab5cafab612e7b595185b81873f18

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Binglong Chen
2. Huaihuo Cao
3. Xiping Zhu
4. J. Lott
5. Bruce Kleiner
6. Reto Muller
7. Le Yin
8. Huiling Gu

In Astronomy and Astrophysics

1. Binglong Chen
2. Huaihuo Cao
3. Xiping Zhu
4. J. Lott
5. Le Yin
6. Bruce Kleiner
7. Reto Muller
8. Huiling Gu

In Geometry and Topology

1. Binglong Chen
2. Huaihuo Cao
3. Bruce Kleiner
4. Xiping Zhu
5. J. Lott
6. Le Yin
7. Reto Muller
8. Detang Zhou

Citations in the corpus

• Strong Uniqueness of the Ricci Flow (2007, methodology): “For an interesting application of this theorem to the theory of Ricci flow with surgery, we refer the readers to see [5] or relevant discussions in [1][10][11].”
• Short-time behaviour of a modified Laplacian coflow of G2-structures (2012, background): “55) From this, it is possible to obtain an expression for Ric (the details can be found in [5, 22], for example) in terms of the background quantities and difference h̄ Ric = Ric− 1 2 ∇̄(2)h+ 1 2 LV̄ ḡ +O ( |h|(2) )”
• Ricci flow coupled with harmonic map flow (2009, background): “More advanced explanations of Perelman’s proof of the two conjectures are given in Cao and Zhu [3] Chow et al.”
• On second variation of Perelman’s Ricci shrinker entropy (2010, neutral): “7 in [6]) If hij = δgij , φ = δf, and η = δτ , then δW(hij , φ, η) = (4πτ) n 2 ( ∫”
• Recent Progress on Ricci Solitons (2009, background): “1 in [17]), which is an improvement of a result of Hamilton (Theorem 26.”
• On the global well-posedness of energy-critical Schr\"odinger equations in curved spaces (2010, background): “, [Cao and Zhu 2006; Chow and Knopf 2004; Chow et al. 2007, 2008; 2010; Hamilton 1982; Morgan and Tian 2007; Shi 1989]) is given by @ @t Rijk` DRijk`C ijk`; (3-1) where”
• Uniqueness and pseudolocality theorems of the mean curvature flow (2007, methodology): “We refer the readers to see an interesting application of this uniqueness theorem to the theory of the Ricci flow with surgery in dimension 3 and 4 [2, 4, 21].”