Winding behaviour of finite-time singularities of the harmonic map heat flow

Mathematische Zeitschrift

Volumn 247, Issue 2, 2004, Pages 279-302

  Topping, Peter ^a  

^a UNIVERSITY OF WARWICK   (United Kingdom)

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EID: 2942614698     PISSN: 00255874     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00209-003-0582-3     Document Type: Article

References (23)

1. Bertsch, M., Dal Passo, R., Van Der Hout, R.: Nonuniqueness for the heat flow of harmonic maps on the disk. Arch. Ration. Mech. Anal. 161, 93-112 (2002)
2. Chang, K.-C.: Heat flow and boundary value problem for harmonic maps. Ann. Inst. Henri Poicaré, Analyse nonlinéaire 6 (5), 363-395 (1989)
3. Chang, K.-C., Ding, W.-Y., Ye, R.: Finite-time Blow-up of the Heat Flow of Harmonic Maps from Surfaces. J. Diff. Geom. 36, 507-515 (1992)
4. Ding, W.-Y., Tian, G.: Energy identity for a class of approximate harmonic maps from surfaces. Comm. Anal. Geom. 3, 543-554 (1995)
5. Eells, J., Lemaire, L.: A report on harmonic maps. Bull. London Math. Soc. 10, 1-68 (1978)
6. Eells, J., Sampson, J.H.: Harmonic mappings of Riemannian manifolds. Am. J. Math. 86, 109-169 (1964)
7. Freire, A.: Uniqueness for the harmonic map flow from surfaces to general targets. Comment. Math. Helv. 70, 310-338 (1995); correction in Comment. Math. Helv. 71, 330-337 (1996)
8. Freire, A.: Uniqueness for the harmonic map flow from surfaces to general targets. Comment. Math. Helv. 70, 310-338 (1995); correction in Comment. Math. Helv. 71, 330-337 (1996)
9. Lemaire, L.: Applications harmoniques de surfaces riemannienes. J. Diff. Geom. 13, 51-78 (1978)
10. Lin, F.-H., Wang, C.-Y.: Energy identity of harmonic map flows from surfaces at finite singular time. Calc. Var. 6, 369-380 (1998)
11. Qing, J.: On singularities of the heat flow for harmonic maps from surfaces into spheres. Comm. Anal. Geom. 3, 297-315 (1995)
12. Qing, J.: A remark on the finite time singularity of the heat flow for harmonic maps. Calc. Var. 17, 393-403 (2003)
13. Qing, J., Tian, G.: Bubbling of the heat flows for harmonic maps from surfaces. Comm. Pure Appl. Math. 50, 295-310 (1997)
14. Sacks, J., Unlenbeck, K.: The existence of minimal immersions of 2-spheres. Ann. Math. 113, 1-24 (1981)
15. Simon, L.: Asymptotics for a class of nonlinear evolution equations, with applications to geometric problems. Ann. Math. 118, 525-571 (1983)
16. Struwe, M.: On the evolution of harmonic mappings of Riemannian surfaces. Comment. Math. Helv. 60, 558-581 (1985)
17. Topping, P.M.: Rigidity in the Harmonic Map Heat Flow. J. Diff. Geom. 45, 593-610 (1997)
18. Topping, P.M.: An example of a nontrivial bubble tree in the harmonic map heat flow. Harmonic morphisms, harmonic maps and related topics (Brest, 1997) CRC Res. Notes Math. 413, 185-191 (2000)
19. Topping, P.M.: Repulsion and quantization in almost-harmonic maps, and asymptotics of the harmonic map flow. To appear, Annals of Math
20. Topping, P.M.: Reverse bubbling and nonuniqueness in the harmonic map flow. Int. Math. Res. Not. 10, 505-520 (2002)
21. Topping, P.M.: The Harmonic Map Heat Flow from Surfaces. PhD Thesis, University of Warwick (1996)
22. Wang, C.-Y.: Bubble phenomena of certain Palais-Smale sequences from surfaces to general targets. Houston J. Math. 22, 559-590 (1996)
23. White, B.: Nonunique tangent maps at isolated singularities of harmonic maps. Bull. Am. Math. Soc. 26, 125-129 (1992)