On weakly harmonic maps and Noether harmonic maps from a Riemann surface into a Riemannian manifold

Frédéric Hélein

Banach Center Publications (1992)

  • Volume: 27, Issue: 1, page 175-181
  • ISSN: 0137-6934

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Hélein, Frédéric. "On weakly harmonic maps and Noether harmonic maps from a Riemann surface into a Riemannian manifold." Banach Center Publications 27.1 (1992): 175-181. <http://eudml.org/doc/262657>.

@article{Hélein1992,
author = {Hélein, Frédéric},
journal = {Banach Center Publications},
keywords = {Noether harmonic map; regularity; weakly harmonic maps; Riemann surface; Riemannian manifold},
language = {eng},
number = {1},
pages = {175-181},
title = {On weakly harmonic maps and Noether harmonic maps from a Riemann surface into a Riemannian manifold},
url = {http://eudml.org/doc/262657},
volume = {27},
year = {1992},
}

TY - JOUR
AU - Hélein, Frédéric
TI - On weakly harmonic maps and Noether harmonic maps from a Riemann surface into a Riemannian manifold
JO - Banach Center Publications
PY - 1992
VL - 27
IS - 1
SP - 175
EP - 181
LA - eng
KW - Noether harmonic map; regularity; weakly harmonic maps; Riemann surface; Riemannian manifold
UR - http://eudml.org/doc/262657
ER -

References

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  2. [BE] P. Baird and J. Eells, A conservation law for harmonic maps, in: Geometry Symposium Utrecht 1980, Lecture Notes in Math. 894, Springer, 1981, 1-25. 
  3. [BC] H. Brezis and J.-M. Coron, Multiple solutions of H-systems and Rellich's conjecture, Comm. Pure Appl. Math. 37 (1984), 149-187. Zbl0537.49022
  4. [Ch] Y.-M. Chen, The weak solutions to the evolution problems of harmonic maps, Math. Z. 201 (1989), 69-74. Zbl0685.58015
  5. [CLMS] R. R. Coifman, P.-L. Lions, Y. Meyer et S. Semmes, Compacité par compensation et espaces de Hardy, C. R. Acad. Sci. Paris Sér. I 309 (1989), 945-949. Zbl0684.46044
  6. [CH] J.-M. Coron and F. Hélein, Harmonic diffeomorphisms, minimizing harmonic maps and rotational symmetry, Compositio Math. 69 (1989), 175-228. Zbl0686.58012
  7. [E] L. C. Evans, Partial regularity for stationary harmonic maps into spheres, preprint. Zbl0754.58007
  8. [Grü] ] M. Grüter, Regularity of weak H-surfaces, J. Reine Angew. Math. 329 (1981), 1-15. 
  9. [H1] F. Hélein, Homéomorphismes quasi conformes entre surfaces riemanniennes, C. R. Acad. Sci. Paris Sér. I 307 (1988), 591-596. 
  10. [H2] F. Hélein, Régularité des applications faiblement harmoniques entre une surface et une sphère, ibid. 311 (1990), 519-524. Zbl0728.35014
  11. [H3] F. Hélein, Regularity of weakly harmonic maps from a surface into a manifold with symmetries, Manuscripta Math. 70 (1991), 203-218. Zbl0718.58019
  12. [H4] F. Hélein, Régularité des applications faiblement harmoniques entre une surface et une variété riemannienne, C. R. Acad. Sci. Paris Sér. I 312 (1991), 591-596. Zbl0728.35015
  13. [HKW] S. Hildebrandt, H. Kaul and K.-O. Widman, An existence theorem for harmonic mappings of Riemannian manifolds, Acta Math. 138 (1977), 1-16. Zbl0356.53015
  14. [J] J. Jost, A note on harmonic maps between surfaces, Ann. Inst. H. Poincaré Anal. Non Linéaire 2 (1985), 397-405. Zbl0585.58011
  15. [KRS] J. Keller, J. Rubinstein and P. Sternberg, Reaction-diffusion processes and evolution to harmonic maps, preprint. Zbl0702.35128
  16. [LU] O. Ladyzhenskaya and N. Ural'tseva, Linear and Quasilinear Elliptic Equations, Academic Press, New York 1968. 
  17. [M] C. B. Morrey, The problem of Plateau on a Riemannian manifold, Ann. of Math. 49 (1948), 807-851, see also C. B. Morrey, Multiple Integrals in the Calculus of Variations, Grundlehren Math. Wiss. 130, Springer, Berlin 1966. Zbl0033.39601
  18. [SaU] J. Sacks and K. Uhlenbeck, The existence of minimal immersions of 2-spheres, Ann. of Math. 113 (1981), 1-24. Zbl0462.58014
  19. [Sc] R. Schoen, Analytic aspects of the harmonic maps problem, in: Math. Sci. Res. Inst. Publ. 2, Springer, Berlin 1984, 321-358. 
  20. [Sh] J. Shatah, Weak solutions and development of singularities of the SU(2) σ-model, Comm. Pure Appl. Math. 41 (1988), 459-469. Zbl0686.35081
  21. [W] H. Wente, An existence theorem for surfaces of constant mean curvature, J. Math. Anal. Appl. 26 (1969), 318-344. Zbl0181.11501

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