Book review of: B. Chow, Ricci solitons in low dimensions. (English) Zbl 07864381
Review of [Zbl 07725933].
MSC:
| 00A17 | External book reviews |
| 53-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to differential geometry |
| 53C15 | General geometric structures on manifolds (almost complex, almost product structures, etc.) |
| 53C25 | Special Riemannian manifolds (Einstein, Sasakian, etc.) |
| 53E20 | Ricci flows |
Citations:
Zbl 07725933References:
| [1] | Bamler, R., Recent developments in Ricci flows, Not. Am. Math. Soc., 68, 9, 1486-1498, 2021 · Zbl 1486.53001 |
| [2] | Bamler, R.; Kleiner, B., Uniqueness and stability of Ricci flow through singularities, Acta Math., 228, 1, 1-215, 2022 · Zbl 1504.53104 · doi:10.4310/ACTA.2022.v228.n1.a1 |
| [3] | Bamler, R.; Kleiner, B., Ricci flow and diffeomorphism groups of 3-manifolds, J. Am. Math. Soc., 36, 2, 563-589, 2023 · Zbl 1518.53072 · doi:10.1090/jams/1003 |
| [4] | Brendle, S.; Schoen, R., Manifolds with \(1/4\)-pinched curvature are space forms, J. Am. Math. Soc., 22, 287-307, 2009 · Zbl 1251.53021 · doi:10.1090/S0894-0347-08-00613-9 |
| [5] | Chow, B., The Ricci flow on the 2-sphere, J. Differ. Geom., 33, 2, 325-334, 1991 · Zbl 0734.53033 · doi:10.4310/jdg/1214446319 |
| [6] | Chow, B.; Chu, S.-C.; Glickenstein, D.; Guenther, C.; Isenberg, J.; Ivey, T.; Knopf, D.; Lu, P.; Luo, F.; Ni, L., The Ricci Flow: Techniques and Applications. Part I. Geometric Aspects, 2007, Providence: Am. Math. Soc., Providence · Zbl 1157.53034 · doi:10.1090/surv/144 |
| [7] | Chow, B.; Chu, S.-C.; Glickenstein, D.; Guenther, C.; Isenberg, J.; Ivey, T.; Knopf, D.; Lu, P.; Luo, F.; Ni, L., The Ricci Flow: Techniques and Applications. Part II. Analytic Aspects, 2008, Providence: Am. Math. Soc., Providence · Zbl 1157.53035 |
| [8] | Chow, B.; Chu, S.-C.; Glickenstein, D.; Guenther, C.; Isenberg, J.; Ivey, T.; Knopf, D.; Lu, P.; Luo, F.; Ni, L., The Ricci Flow: Techniques and Applications. Part III. Geometric-Analytic Aspects, 2010, Providence: Am. Math. Soc., Providence · Zbl 1216.53057 · doi:10.1090/surv/163 |
| [9] | Chow, B.; Chu, S.-C.; Glickenstein, D.; Guenther, C.; Isenberg, J.; Ivey, T.; Knopf, D.; Lu, P.; Luo, F.; Ni, L., The Ricci Flow: Techniques and Applications. Part IV. Long-Time Solutions and Related Topics, 2015, Providence: Am. Math. Soc., Providence · Zbl 1341.53001 · doi:10.1090/surv/206 |
| [10] | Hamilton, R. S., Three-manifolds with positive Ricci curvature, J. Differ. Geom., 17, 2, 255-306, 1982 · Zbl 0504.53034 · doi:10.4310/jdg/1214436922 |
| [11] | Hamilton, R. S., The Ricci Flow on Surfaces, Mathematics and General Relativity, 237-262, 1988, Providence: Am. Math. Soc., Providence · Zbl 0663.53031 · doi:10.1090/conm/071/954419 |
| [12] | Perelman, G.: The entropy formula for the Ricci flow and its geometric applications (2002). arXiv:math/0211159. preprint · Zbl 1130.53001 |
| [13] | Perelman, G.: Ricci flow with surgery on three-manifolds (2003). arXiv:math/0303109. Preprint · Zbl 1130.53002 |
| [14] | Perelman, G.: Finite extinction time for the solutions to the Ricci flow on certain three-manifolds (2003). arXiv:math/0307245. Preprint · Zbl 1130.53003 |
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