Homotopy classes in Sobolev spaces and energy minimizing maps

White, Brian

doi:10.1090/S0273-0979-1985-15407-2

Homotopy classes in Sobolev spaces and energy minimizing maps
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Bull. Amer. Math. Soc. 13 (1985), 166-168

References

James Eells and Luc Lemaire, Selected topics in harmonic maps, CBMS Regional Conference Series in Mathematics, vol. 50, Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 1983. MR 703510, DOI 10.1090/cbms/050
James Eells Jr. and J. H. Sampson, Harmonic mappings of Riemannian manifolds, Amer. J. Math. 86 (1964), 109–160. MR 164306, DOI 10.2307/2373037
Herbert Federer, Geometric measure theory, Die Grundlehren der mathematischen Wissenschaften, Band 153, Springer-Verlag New York, Inc., New York, 1969. MR 0257325
J. Sacks and K. Uhlenbeck, The existence of minimal immersions of $2$-spheres, Ann. of Math. (2) 113 (1981), no. 1, 1–24. MR 604040, DOI 10.2307/1971131
Richard Schoen and Karen Uhlenbeck, A regularity theory for harmonic maps, J. Differential Geometry 17 (1982), no. 2, 307–335. MR 664498
Richard Schoen and Karen Uhlenbeck, Boundary regularity and the Dirichlet problem for harmonic maps, J. Differential Geom. 18 (1983), no. 2, 253–268. MR 710054
R. Schoen and Shing Tung Yau, Existence of incompressible minimal surfaces and the topology of three-dimensional manifolds with nonnegative scalar curvature, Ann. of Math. (2) 110 (1979), no. 1, 127–142. MR 541332, DOI 10.2307/1971247
Brian White, Mappings that minimize area in their homotopy classes, J. Differential Geom. 20 (1984), no. 2, 433–446. MR 788287
Brian White, Infima of energy functionals in homotopy classes of mappings, J. Differential Geom. 23 (1986), no. 2, 127–142. MR 845702