Harmonic diffeomorphisms, minimizing harmonic maps and rotational symmetry
Compositio Mathematica, Volume 69 (1989) no. 2, p. 175-228
@article{CM_1989__69_2_175_0,
author = {Coron, Jean-Michel and Helein, Fr\'ed\'eric},
title = {Harmonic diffeomorphisms, minimizing harmonic maps and rotational symmetry},
journal = {Compositio Mathematica},
volume = {69},
number = {2},
year = {1989},
pages = {175-228},
zbl = {0686.58012},
mrnumber = {984634},
language = {en},
url = {http://www.numdam.org/item/CM_1989__69_2_175_0}
}

Coron, J. M.; Helein, F. Harmonic diffeomorphisms, minimizing harmonic maps and rotational symmetry. Compositio Mathematica, Volume 69 (1989) no. 2, pp. 175-228. http://www.numdam.org/item/CM_1989__69_2_175_0/

[ABL] F. Almgren, W. Browder and E.H. Lieb: Coarea, liquid crystals, and minimal surfaces, DD7-A selection of Papers, Springer-Verlag, New-York, 1987.

[B1] P. Baird: Harmonic morphisms into Riemann surfaces and generalized analytic functions, Ann. Inst. Fourier, Grenoble 37(1) (1987) 137-173. | Numdam | MR 894564 | Zbl 0608.58015

[B2] P. Baird: Harmonic maps with symmetry, harmonic morphisms and deformations of metrics Research Notes in Math. 87, Pitman (1983). | MR 716320 | Zbl 0515.58010

[BE] P. Baird and J. Eells: A conservation law for harmonic maps, geometry, Symp. Utrecht (1980), Lecture Notes in Math. 894, Springer-Verlag (1981), pp. 1-25. | MR 655417 | Zbl 0485.58008

[BW] P. Baird and J.C. Wood: Bernstein theorems for harmonic morphisms from R3 and S3, Math. Ann. 280 (1988) 579-603. | MR 939920 | Zbl 0621.58011

[B] A. Baldes, Stability and uniqueness properties of the equator map from a ball into an ellipsoid, Math. Z. 185 (1984), 505-516. | MR 733770 | Zbl 0513.58021

[BCD] A. Bernard, E.A. Campbell and A.M. Davie: Brownian motion and generalized analytic and inner functions, Ann. Inst. Fourier, Grenoble, 29(1) (1979) 207-208. | Numdam | MR 526785 | Zbl 0386.30029

[BZ] F. Bethuel and X. Zheng: Density of smooth functions between two manifolds in Sobolev spaces, J. Funct. Analysis, to appear. | MR 960223 | Zbl 0657.46027

[BCL] H. Brezis, J.M. Coron and E. Lieb, Harmonic maps with defects, Commun. Math. Phys. 107 (1986) 649-705. | MR 868739 | Zbl 0608.58016

[CG] J.M. Coron and R. Gulliver: Minimizing p-Harmonic maps into spheres, preprint. | MR 1018054

[EL] J. Eells and L. Lemaire: Report on harmonic maps, Bull. London Math. Soc. 10 (1978) 1-68. | MR 495450 | Zbl 0401.58003

[ES] J. Eells and J.H. Sampson: Harmonic mappings of Riemannian manifolds, Amer. J. Math. 86 (1964) 109-160. | MR 164306 | Zbl 0122.40102

[F] H. Federer: Geometric Measure Theory, Berlin- Heidelberg-New-York, Springer (1969). | MR 257325 | Zbl 0176.00801

[GW] R. Gulliver and B. White: The rate of convergence of a harmonic map at a singular point, Math. Ann. (to appear). | MR 990588 | Zbl 0645.58018

[Ham] R. Hamilton: Harmonic maps of manifolds with boundary, Lectures Notes in Math. Springer-Verlag 471 (1975). | MR 482822 | Zbl 0308.35003

[HKL] R. Hardt, D. Kinderlehrer and F.H. Lin, Existence and partial regularity of static liquid crystal configurations, Commun. Math. Phys. 105 (1986) 547-570. | MR 852090 | Zbl 0611.35077

[HL] R. Hardt and F.H. Lin: Mappings that minimize the pth power of the gradient, preprint.

[Ha1] P. Hartman: On homotopic harmonic maps, Canad. J. Math. 19 (1967) 673-687. | MR 214004 | Zbl 0148.42404

[Ha2] P. Hartman: Ordinary differential equations, New-York (1964). | MR 171038 | Zbl 0125.32102

[He] F. Hélein: Regularity and uniqueness of harmonic maps into an ellipsoid, Manuscripta Math. 60 (1988) 235-257. | MR 924091 | Zbl 0646.58020

[JK] W. Jäger and H. Kaul: Rotationally symmetric harmonic maps from a ball into a sphere and the regularity problem for weak solutions of elliptic systems, J. Reine Angew. Math. 343 (1983) 146-161. | MR 705882 | Zbl 0516.35032

[J] J. Jost: Harmonic maps between surfaces, Lectures Notes in Math., Springer Verlag, 1062 (1984). | MR 754769 | Zbl 0542.58002

[JS] J. Jost and R. Schoen: On the existence of harmonic diffeomorphisms between surfaces Inv. Math. 66 (1982) 549-561. | MR 656629 | Zbl 0488.58009

[La] J.P. La Salle: Stability theory for ordinary differential equations, J. Differential Equations 4 (1968) 57-65. | MR 222402 | Zbl 0159.12002

[Le1] L. Lemaire: Applications harmoniques de surfaces Riemanniennes, J. Diff. Geom. 13 (1978) 51-78. | MR 520601 | Zbl 0388.58003

[Le2] L. Lemaire: Boundary value problems for harmonic maps and minimal maps of surfaces into manifolds, Ann. Scuola Norm. Sup. Pisa 9 (1982) 91-103. | Numdam | MR 664104 | Zbl 0532.58004

[Li] F.H. Lin: A remark on the map x/|x|, C.R. Acad. Sci. Paris, t. 305, Série I (1987), pp. 529-531. | MR 916327 | Zbl 0652.58022

[M] C.B. Morrey: The problem of Plateau on a Riemannian manifold, Ann. of Math. 49 (1948) 807-851. | MR 27137 | Zbl 0033.39601

[SU] J. Sacks and K. Uhlenbeck: The existence of minimal immersions of 2-spheres, Ann. of Math. 113 (1981) 1-24. | MR 604040 | Zbl 0462.58014

[S1] R. Schoen: Analytic aspects of the harmonic map problem, Seminar on Nonlinear Partial Differential Equations, edited by S.S. Chern, MAth. sc. Research Institute Publications. | Zbl 0551.58011

[S2] R. Schoen: Existence and regularity for some geometric variational problems, Thesis Stanford Univ. (1977).