On rotationally invariant shrinking Ricci solitons

Pacific Journal of Mathematics

Volumn 236, Issue 1, 2008, Pages 73-88

  Kotschwar, Brett ^a  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Ricci flow; Ricci solitons

Indexed keywords

EID: 51549105164     PISSN: 00308730     EISSN: None     Source Type: Journal    
DOI: 10.2140/pjm.2008.236.73     Document Type: Article

References (14)

1. C. Böhm and B. Wilking, "Manifolds with positive curvature are space forms", preprint, 2006. To appear in Ann. of Math. arXiv math/0606187v1
2. R. Bryant, unpublished notes on Ricci solitons, most of whose contents appear in [Ivey 1992].
3. X. Chen, P. Lu, and G. Tian, "A note on uniformization of Riemann surfaces by Ricci flow", Proc. Amer. Math. Soc. 134:11 (2006), 3391-3393. MR 2007d:53109 Zbl 1113.53042
4. B. Chow and D. Knopf, The Ricci flow: an introduction, Mathematical Surveys and Monographs 110, American Mathematical Society, Providence, RI, 2004. MR 2005e: 53101 Zbl 1086.53085
5. B. Chow, S.-C. Chu, D. Glickenstein, C. Guenther, J. Isenberg, T. Ivey, D. Knopf, P. Lu, F. Luo, and L. Ni, The Ricci flow: techniques and applications, I: Geometric aspects, Mathematical Surveys and Monographs 135, American Mathematical Society, Providence, RI, 2007. MR 2302600 Zbl 05149301
6. M. Feldman, T. Ilmanen, and D. Knopf, "Rotationally symmetric shrinking and expanding gradient Kähler-Ricci solitons", J. Differential Geom. 65:2 (2003), 169-209. MR 2005e:53102 Zbl 1069.53036
7. R. S. Hamilton, "Four-manifolds with positive curvature operator", J. Differential Geom. 24:2 (1986), 153-179. MR 87m:53055 Zbl 0628.53042
8. R. S. Hamilton, "The Ricci flow on surfaces", pp. 237-262 in Mathematics and general relativity (Santa Cruz, CA, 1986), edited by J. A. Isenberg, Contemp. Math. 71, Amer. Math. Soc., Providence, RI, 1988. MR 89i:53029 Zbl 0663.53031
9. R. S. Hamilton, "The formation of singularities in the Ricci flow", pp. 7-136 in Surveys in differential geometry (Cambridge, MA, 1993), vol. 2, edited by C.-C. Hsiung and S.-T. Yau, Int. Press, Cambridge, MA, 1995. MR 97e:53075 Zbl 0867.53030
10. T. Ivey, On solitons for the Ricci flow, PhD thesis, Duke University, 1992.
11. N. Koiso, "On rotationally symmetric Hamilton's equation for Kähler-Einstein metrics", pp. 327-337 in Recent topics in differential and analytic geometry, edited by T. Ochiai, Adv. Stud. Pure Math. 18, Academic Press, Boston, 1990. MR 93d:53057 Zbl 0739.53052
12. B. Kotschwar, Some results on the qualitative behavior of solutions to the Ricci flow and other geometric evolution equations, PhD thesis, University of California at San Diego, 2007.
13. L. Ni, "Ancient solutions to Kähler-Ricci flow", Math. Res. Lett. 12:5-6 (2005), 633-653. MR 2006i:53097 Zbl 1087.53061
14. G. Perelman, "Ricci flow with surgery on three-manifolds" , Preprint, 2003. arXiv math.DG/0303109v1