The Blow-up Locus of Heat Flows for Harmonic Maps

Acta Mathematica Sinica, English Series

Volumn 16, Issue 1, 2000, Pages 29-62

  Li, Jiayu ^a   Tian, Gang ^b  

^a INSTITUTE OF GEOLOGY AND GEOPHYSICS   (China)

^b MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Blow up locus; Brakke motion; Heat flow; Mean curvature flow

Indexed keywords

EID: 0346206377     PISSN: 14398516     EISSN: None     Source Type: Journal    
DOI: 10.1007/s101149900024     Document Type: Article

References (26)

1. L Ambrosio, H M Soner. Level set approach to mean curvature flow in arbitrary codimension. J Diff Geom, 1996, 43: 693-737
2. K Brakke. The Motion of a Surface by its Mean Curvature. Princeton Univ Press, 1978
3. T Ilmanen. Elliptic regularization and partial regularity for motion by mean curvature. Memoirs of the Amer Math Soc, 520, 1994
4. 2. Nemantics Coron J-M et al ed, Kluwer Academic Publishers, 1990, 37-48
5. J Li, G Tian. A blow-up formula for stationary harmonic maps. IMRN 1998,14: 735-755
6. M Struwe. On the evolution of harmonic mappings of Riemannian surfaces. Comm Math Hel 1985, 60: 558-581
7. J Qing. On singularities of the heat flow for harmonic maps from surfaces into spheres. Comm Anal Geom, 1995, 3: 297-315
8. W Ding, G Tian. Energy identity for a class of approximate harmonic maps from surfaces. Comm Anal Geom, 1995, 4: 543-554
9. M Struwe. On the evolution of harmonic maps in higher dimensions. J Diff Geom, 1988, 28: 485-502
10. Y Chen, J Li, F Lin. Partial regularity for weak heat flows into spheres. Comm Pure Appl math, XLVIII 1995, 429-448
11. M Feldman. Partial regularity for harmonic maps of evolution into spheres. Comm Partial Diff Equat, 1994, 19: 761-790
12. X Liu. Partial regularity for weak heat flows into general compact Riemannian manifolds. in press
13. F Bethuel. On the singular set of stationary harmonic maps. Manu Math, 1993, 78: 417-443
14. Y Chen, M Struwe. Existence and partial regularity for heat flow for harmonic maps. Math Z 1989, 201: 83-103
15. F H Lin, C Y Wang. Harmonic and quasi-harmonic spheres. Comm Anal Geom, to appear
16. W -Y Ding. Blow-up of solutions of heat flow for harmonic maps. Advin Math, 1990, 19: 80-92
17. L Simon. Lectures on geometric measure theory. Proc Center Math Anal, 1983, 3, Australian National Univ Press
18. n; distribution, rectifiability, and densities. Ann of Math, 1987, 125: 537-643
19. F -H Lin. Gradient estimates and blow-up analysis for stationary harmonic maps I. in press
20. J Sacks, K Uhlenbeck. The existence of minimal immersions of two spheres. Ann Math, 1981, 113: 1-24
21. W Allard. On the first variation of a varifold. Ann Math 1972, 95: 417-491
22. X Cheng. Estimate of the singular set of the evolution problem for harmonic maps. J Diff Geom, 1991, 34: 169-174
23. J Eells, J H Sampson. Harmonic mappings of Riemannian manifolds. Amer J Math, 1964, 86: 109-160
24. J -M Coron, J -M Ghidaglia. Explosion en temps fini pour le flot des applications harmonique. C R Acad Sci Paris, Serie I, 1989, 308: 339-344
25. Y Chen, W -Y Ding. Blow-up and global existence for heat flows of harmonic maps. Invent Math 1990, 99: 567-578
26. K Chang, W Ding, R Ye. Finite time blow-up of the heat flow of harmonic maps. J Diff Geom, 1992, 36: 507-515