Entropy and reduced distance for Ricci expanders

Journal of Geometric Analysis

Volumn 15, Issue 1, 2005, Pages 49-62

  Feldman, Michael ^a,b   Ilmanen, Tom ^a,b   Ni, Lei ^c  

^a UNIVERSITY OF WISCONSIN MADISON   (United States)

^b ETH ZURICH   (Switzerland)

^c UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

asymptotic behavior; Entropy; Li Yau Hamilton inequalit; monotonicity; reduced volume; Ricci expanders; Ricci flow

Indexed keywords

EID: 23744500873     PISSN: 10506926     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02921858     Document Type: Article

References (30)

1. 2 structure of moduli spaces of Einstein metrics on 4-manifolds,Geom. Funct. Anal. 2, 29-89, (1992).
2. 3,Comm. Part. Diff. Eq. 20, 1937-1958, (1995).
3. Barnes, I. and Ilmanen, T. unpublished computer study, (1994).
4. Cao, H.-D., Hamilton, R. S., and Ilmanen, T. Gaussian densities and stability for some Ricci solitons, math.DG/ 0404165, April (2004).
5. Cheeger, J. and Colding, T. H. On the structure of spaces with Ricci curvature bounded below. I,J. Differential Geom. 46, 406-480, (1997). (Pubitemid 127338748)
6. Cheeger, J. and Tian, G. Collapsing and noncollapsing of Einstein 4-manifolds, in preparation, (2004).
7. Chow, B., Chu, S.-C., Lu, P., and Ni, L. Notes on Perelman's articles on Ricci flow.
8. Chow, B. and Knopf, D. The Ricci flow, vol. I: An introduction, Math. Surveys and Monographs,AMS 110, (2004).
9. 2, preprint, (2004).
10. Feldman, M., Ilmanen, T., and Knopf, D. Rotationally symmetric shrinking and expanding gradient Kähler-Ricci solitons,J. Differential Geom. 65, 169-209,(2003). (Pubitemid 38845910)
11. Hamilton, R. S. The Harnack estimate for the Ricci flow,J. Differential Geom. 37, 225-243, (1993).
12. Hamilton, R. S. A compactness property for solutions of the Ricci flow,Amer. J. Math. 117, 545-572, (1995).
13. Hamilton, R. S. Non-singular solutions of Ricci flow on three-manifolds,Comm. Anal. Geom. 7, 695-729, (1999).
14. Hong, M.-C. and Tian, G. Asymptotical behavior of the Yang-Mills flow and singular Yang-Mills connections,Math. Ann., to appear.
15. Huisken, G. Asymptotic behavior for singularities of the mean curvature flow,J. Differential Geom. 31, 285-299, (1990).
16. Ilmanen, T. Elliptic regularization and partial regularity for motion by mean curvature,Mem. Amer. Math. Soc. #520, (1994).
17. Ilmanen, T. Singularities of mean curvature flow of surfaces, preprint, http://www.math.ethz.ch/~ ilmanen/papers/pub.htm, (1995).
18. Ilmanen, T. Lectures on mean curvature flow and related equations, Lecture Notes, ICTP, Trieste, http:// www.math.ethz.ch/~ilmanen/papers/pub.html, (1995).
19. Ilmanen, T. Notes on mean curvature flow, in preparation,(2004).
20. Li, P. and Yau, S.-T. On the parabolic kernel of the Schrödinger operator,Acta Math. 156, 153-201, (1986).
21. Nash, J. Continuity of solutions of parabolic and elliptic equations,Amer. J. Math. 80, 935-954, (1958).
22. Ni, L. The entropy formula for linear heat equation,J. Geom. Anal. 14(1), 87-100, (2004).
23. Ni, L. Addenda to The entropy formula for linear heat equation,J. Geom. Anal. 14(2), 369-374, (2004).
24. Ni, L. A new matrix Li-Yau-Hamilton inequality for Kahler-Ricci flow, submitted.
25. Perelman, G. The entropy formula for the Ricci flow and its geometric applications, math.DG/ 0211159, November (2002).
26. Perelman, G. Ricci flow with surgery on three-manifolds, math.DG/0303109, March (2003).
27. Sesum, N. Limiting behavior of the Ricci flow, preprint, (2004).
28. Uhlenbeck, K. Removable singularities in Yang-Mills fields,Comm. Math. Phys. 83, 11-29, (1982).
29. Weinkove, B. A complex Frobenuis theorem, multiplier ideal sheaves and Hermitian-Einstein metrics on stable bundles, preprint, (2003).
30. White, B. personal communication, (2000).