Repulsion and quantization in almost-harmonic maps, and asymptotics of the harmonic map flow

Annals of Mathematics

Volumn 159, Issue 2, 2004, Pages 465-534

  Topping, Peter ^a  

^a UNIVERSITY OF WARWICK   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 4644221893     PISSN: 0003486X     EISSN: None     Source Type: Journal    
DOI: 10.4007/annals.2004.159.465     Document Type: Review

References (18)

1. W.-Y. DING and G. TIAN, Energy identity for a class of approximate harmonic maps from surfaces, Comm. Anal. Geom. 3 (1995), 543-554.
2. J. EELLS and L. LEMAIRE, A report on harmonic maps, Bull. London Math. Soc. 10 (1978), 1-68.
3. J. EELLS and J. H. SAMPSON, Harmonic mappings of Riemannian manifold, Amer. J. Math. 86 (1964), 109-169.
4. D. GILBARG and N. S. TRUDINGER, Elliptic Partial Differential Equations of Second Order (Second edition), Springer-Verlag, New York (1983).
5. F.-H. LIN and C.-Y. WANG, Energy identity of harmonic map flows from surfaces at finite singular time, Calc. Var. Partial Differential Equations 6 (1998), 369-380.
6. T. H. PARKER, Bubble tree convergence for harmonic maps, J. Differential Geom. 44 (1996), 595-633.
7. J. QING, On singularities of the heat flow for harmonic maps from surfaces into spheres, Comm. Anal. Geom. 3 (1995), 297-315.
8. J. QING and G. TIAN, Bubbling of the heat flows for harmonic maps from surface, Comm. Pure Appl. Math. 50 (1997), 295-310.
9. J. SACKS and K. UHLENBECK, The existence of minimal immersions of 2-spheres, Ann. of Math. 113 (1981), 1-24.
10. G. Segal, The topology of spaces of rational functions, Acta Math. 143 (1979), 39-72.
11. L. SIMON, Asymptotics for a class of nonlinear evolution equations, with applications to geometric problems, Ann. of Math. 118 (1983), 525-571.
12. E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton University Press, Prinecton, NJ (1970).
13. M. STRUWE, On the evolution of harmonic mappings of Riemannian surfaces, Comment. Math. Helv. 60 (1985) 558-581.
14. P. M. TOPPING, The harmonic map heat flow from surfaces, Ph.D. Thesis, University of Warwick (1996).
15. _, Rigidity in the harmonic map heat flow, J. Differential Geom. 45 (1997), 593-610.
16. P. M. TOPPING, Bubbling of almost-harmonic maps between 2-spheres at points of zero energy density, preprint (2002).
17. C.-Y. WANG, Bubble phenomena of certain Palais-Smale sequences from surfaces to general targets, Houston J. Math. 22 (1996), 559-590.
18. W. P. Ziemer, Weakly Differentiable Functions, Graduate Texts in Math. 120, Springer-Verlag, New York (1989).