Bulletin (New Series) of the American Mathematical Society

Homotopy classes in Sobolev spaces and energy minimizing maps

Brian White

Full-text: Open access

Article information

Source
Bull. Amer. Math. Soc. (N.S.), Volume 13, Number 2 (1985), 166-168.

Dates
First available in Project Euclid: 4 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.bams/1183552702

Mathematical Reviews number (MathSciNet)
MR799804

Zentralblatt MATH identifier
0595.58011

Subjects
Primary: 58E20: Harmonic maps [See also 53C43], etc. 55P10: Homotopy equivalences
Secondary: 46E35: Sobolev spaces and other spaces of "smooth" functions, embedding theorems, trace theorems

Citation

White, Brian. Homotopy classes in Sobolev spaces and energy minimizing maps. Bull. Amer. Math. Soc. (N.S.) 13 (1985), no. 2, 166--168. https://projecteuclid.org/euclid.bams/1183552702


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References

  • [EL] J. Eells and L. Lemaire, Selected topics in harmonic maps, CBMS Regional Conf. Ser. in Math., no. 50, Amer. Math. Soc., Providence, R. I., 1983.
  • [ES] J. Eells and J. Sampson, Harmonic mappings of Riemannian manifolds, Amer. J. Math. 86 (1964), 109-160.
  • [F] H. Federer, Geometric measure theory, Springer-Verlag, Berlin-Heidelberg-New York, 1969.
  • [SU] J. Sacks and K. Uhlenbeck, The existence of minimal 2-spheres, Ann. of Math. (2) 113 (1981), 1-24.
  • [SU1] R. Schoen and K. Uhlenbeck, A regularity theory for harmonic maps, J. Differential Geom. 17 (1982), 307-335.
  • [SU2] R. Schoen and K. Uhlenbeck, Boundary regularity and the Dirichlet problem for harmonic maps, J. Differential Geom. 18 (1983), 253-268.
  • [SY] R. Schoen and S. T. Yau, Existence of incompressible minimal surfaces and the topology of three-dimensional manifolds with non-negative scalar curvature, Ann. of Math. (2) 110 (1979), 127-142.
  • [W1] B. White, Mappings that minimize area in their homotopy classes, J. Differential Geom. (to appear).
  • [W2] B. White, Infima of energy functionals in homotopy classes of mappings, preprint.
  • [W3] B. White, Mappings that minimize energy functionals in their homotopy classes (in preparation).