@article{CM_1989__69_2_175_0, author = {Coron, J. M. and Helein, F.}, title = {Harmonic diffeomorphisms, minimizing harmonic maps and rotational symmetry}, journal = {Compositio Mathematica}, pages = {175--228}, publisher = {Kluwer Academic Publishers}, volume = {69}, number = {2}, year = {1989}, mrnumber = {984634}, zbl = {0686.58012}, language = {en}, url = {http://www.numdam.org/item/CM_1989__69_2_175_0/} }

TY - JOUR AU - Coron, J. M. AU - Helein, F. TI - Harmonic diffeomorphisms, minimizing harmonic maps and rotational symmetry JO - Compositio Mathematica PY - 1989 SP - 175 EP - 228 VL - 69 IS - 2 PB - Kluwer Academic Publishers UR - http://www.numdam.org/item/CM_1989__69_2_175_0/ LA - en ID - CM_1989__69_2_175_0 ER -

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] Coarea, liquid crystals, and minimal surfaces, DD7-A selection of Papers, Springer-Verlag, New-York, 1987.

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

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

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

and :[BW] Bernstein theorems for harmonic morphisms from R3 and S3, Math. Ann. 280 (1988) 579-603. | MR | Zbl

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

,[BCD] Brownian motion and generalized analytic and inner functions, Ann. Inst. Fourier, Grenoble, 29(1) (1979) 207-208. | Numdam | MR | Zbl

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

and :[BCL] Harmonic maps with defects, Commun. Math. Phys. 107 (1986) 649-705. | MR | Zbl

, and ,[CG] Minimizing p-Harmonic maps into spheres, preprint. | MR

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

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

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

:[GW] The rate of convergence of a harmonic map at a singular point, Math. Ann. (to appear). | MR | Zbl

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

:[HKL] Existence and partial regularity of static liquid crystal configurations, Commun. Math. Phys. 105 (1986) 547-570. | MR | Zbl

, and ,[HL] Mappings that minimize the pth power of the gradient, preprint.

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

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

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

:[JK] 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 | Zbl

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

:[JS] On the existence of harmonic diffeomorphisms between surfaces Inv. Math. 66 (1982) 549-561. | MR | Zbl

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

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

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

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

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

:[SU] The existence of minimal immersions of 2-spheres, Ann. of Math. 113 (1981) 1-24. | MR | Zbl

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

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

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