Some conformal properties of p-harmonic maps and a regularity for sphere-valued p-harmonic maps

Hiroshi TAKEUCHI

doi:10.2969/jmsj/04620217

Hiroshi TAKEUCHI

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JOURNAL FREE ACCESS

1994 Volume 46 Issue 2 Pages 217-234

DOI https://doi.org/10.2969/jmsj/04620217

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Published: 1994 Received: July 10, 1992 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) P. Baird, Harmonic maps with symmetry, harmonic morphism and deformations of metrics, Research notes in Math., 87, Pitman, 1983.
2) P. Baird and J. Eells, A conservation law for harmonic maps, in Geometry symposium, Proceedings, Utrecht 1980, (eds. E. Looijenga, D. Siersma and F. Takens), Lecture Notes in Math., 894, Springer, 1981, pp. 1-25.
3) J. M. Coron and R. D. Gulliver, Minimizing p-harmonic maps into spheres, J. Reine Angew. Math., 401 (1989), 82-100.
4) F. Duzaar and M. Fuchs, Existence and regularity of functions which minimize certain energies in homotopy classes of mappings, Asymptotic Analysis, 5 (1991), 129-144.
5) J. Eells and L. Lemaire, Selected topics in harmonic maps, C.B.M.S. Regional conference series, Amer. Math. Soc., 50, 1983.
6) J. Eells and J.H. Sampson, Harmonic mappings of Riemannian manifolds, Amer. J. Math., 86 (1964), 109-160.
7) L. C. Evans, Partial regularity for stationary harmonic maps into spheres, Arch. Rational Mech. Anal., 116 (1991), 101-113.
8) N. Fusco and J. Hutchinson, Partial regularity results for minimizers of certain functionals having non quadratic growth, Ann. Math. Pure Appl., 155 (1989),1-24.
9) M. Giaquinta, Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic systems, Ann. of Math. Stud., 105, Princeton Univ. Press, 1983.
10) R. Hardt and F. H. Lin, Mapping minimizing the L^p norm of the gradient, Comm. Pure Appl. Math., 40 (1987), 555-588.
11) F. Helein, Régularité des applications faiblement harmoniques entre une surface et une sphère, C. R. Acad. Sci. Paris, 311 (1990), 519-524.
12) S. Luckhaus, Partial Hölder continuity for minima of certain energies among maps into Riemannian manifold, Indiana Univ. Math. J., 37 (1988), 346-367.
13) P. Price, A monotonicity formula for Yang-Mills fields, Manuscripta Math., 43 (1983), 131-166.
14) R. Schoen, Analytic aspect of the harmonic map problem, In Seminar on Nonlinear Partial Differential Equations, (ed. S.S. Chern), Springer, 1984, pp. 321-358.
15) S. Takakuwa, On removable singularities of stationary harmonic maps, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 32 (1985), 373-395.
16) H. Takeuchi, Stability and Liouville theorems of P-harmonic maps, Japan. J. Math., 17 (1991), 317-332.
17) K. Uhlenbeck, Regularity for a class of nonlinear elliptic systems, Acta Math., 138 (1977), 219-240.

Right : [1] P. Baird, Harmonic maps with symmetry, harmonic morphism and deformations of metrics, Research notes in Math., 87, Pitman, 1983.
[2] P. Baird and J. Eells, A conservation law for harmonic maps, In Geometry symposium, Proceedings, Utrecht 1980, (eds. E. Looijenga, D. Siersma and F. Takens), Lecture Notes in Math., 894, Springer, 1981, pp. 1-25.
[3] J. M. Coron and R. D. Gulliver, Minimizing p-harmonic maps into spheres, J. Reine Angew. Math., 401 (1989), 82-100.
[4] F. Duzaar and M. Fuchs, Existence and regularity of functions which minimize certain energies in homotopy classes of mappings, Asymptotic Analysis, 5 (1991), 129-144.
[5] J. Eells and L. Lemaire, Selected topics in harmonic maps, C. B. M. S. Regional conference series, Amer. Math. Soc., 50, 1983.
[6] J. Eells and J. H. Sampson, Harmonic mappings of Riemannian manifolds, Amer. J. Math., 86 (1964), 109-160.
[7] L. C. Evans, Partial regularity for stationary harmonic maps into spheres, Arch. Rational Mech. Anal., 116 (1991), 101-113.
[8] N. Fusco and J. Hutchinson, Partial regularity results for minimizers of certain functionals having non quadratic growth, Ann. Math. Pure Appl., 155 (1989),1-24.
[9] M. Giaquinta, Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic systems, Ann. of Math. Stud., 105, Princeton Univ. Press, 1983.
[10] R. Hardt and F. H. Lin, Mapping minimizing the L^p norm of the gradient, Comm. Pure Appl. Math., 40 (1987), 555-588.
[11] F. Helein, Régularité des applications faiblement harmoniques entre une surface et une sphère, C. R. Acad. Sci. Paris, 311 (1990), 519-524.
[12] S. Luckhaus, Partial Hölder continuity for minima of certain energies among maps into Riemannian manifold, Indiana Univ. Math. J., 37 (1988), 346-367.
[13] P. Price, A monotonicity formula for Yang-Mills fields, Manuscripta Math., 43 (1983), 131-166.
[14] R. Schoen, Analytic aspect of the harmonic map problem, In Seminar on Nonlinear Partial Differential Equations, (ed. S. S. Chern), Springer, 1984, pp. 321-358.
[15] S. Takakuwa, On removable singularities of stationary harmonic maps, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 32 (1985), 373-395.
[16] H. Takeuchi, Stability and Liouville theorems of P-harmonic maps, Japan. J. Math., 17 (1991), 317-332.
[17] K. Uhlenbeck, Regularity for a class of nonlinear elliptic systems, Acta Math., 138 (1977), 219-240.

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