The Formation of Singularities in the Harmonic Map Heat Flow

Communications in Analysis and Geometry

Volumn 4, Issue 4, 1996, Pages 526-546

  Grayson, Matthew ^a   Hamilton, Richard S ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0041719918     PISSN: 10198385     EISSN: None     Source Type: Journal    
DOI: 10.4310/cag.1996.v4.n4.a1     Document Type: Article

References (11)

1. K.-C. Chang, W.-Y. Ding and R. Ye, Finite time blow-up of the heat flow of harmonic maps from surfaces, preprint.
2. Y. Chen and M. Struwe(1989), Existence and partial regularity for the solutions to evolution problems for harmonic maps, Math. Z.,201,83-103.
3. J. Eells and J.H. Sampson (1964), Harmonic mappings of Riemannian manifolds, Amer. J. Math., 86,109-160.
4. R.S. Hamilton, Monotonicity principles for evolution equations in geometry, preprint.
5. R.S. Hamilton, A matrix Harnack estimate for the heat equation, preprint.
6. G. Huisken(1990),Asymptotic Behavior for singularities of the mean curvature flow, J. Diff. Geom., 31, 285-299.
7. P. Li and S.-T. Yau(1986), On the parabolic kernel of the Schrödinger operator, Acta Math., 156, 153-201.
8. W.-X. Shi(1989), Deforming the metric on complete Riemmanian manifolds, J. Diff. Geom., 30, 223-301.
9. W.-X. Shi(1989), Ricci deformation of the metric on complete non-compact Riemannian manifolds, J. Diff. Geom., 30, 303-394.
10. M. Struwe(1985), On the evolution of harmonic maps of Riemannian surfaces, Comm. Math. Helv., 60, 558-581.
11. M. Struwe(1988), On the evolution of harmonic maps in higher dimensions, J. Diff. Geom., 28, 485-502.