Some properties and applications of harmonic mappings
Sampson, J. H.
Annales scientifiques de l'École Normale Supérieure, Tome 11 (1978), p. 211-228 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{ASENS_1978_4_11_2_211_0,
     author = {Sampson, Joseph H.},
     title = {Some properties and applications of harmonic mappings},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     volume = {11},
     year = {1978},
     pages = {211-228},
     doi = {10.24033/asens.1344},
     mrnumber = {80b:58031},
     zbl = {0392.31009},
     language = {en},
     url = {http://dml.mathdoc.fr/item/ASENS_1978_4_11_2_211_0}
}

Sampson, J. H. Some properties and applications of harmonic mappings. Annales scientifiques de l'École Normale Supérieure, Tome 11 (1978) pp. 211-228. doi : 10.24033/asens.1344. http://gdmltest.u-ga.fr/item/ASENS_1978_4_11_2_211_0/

[1] N. Aronszajn, A Unique Continuation Theorem for Solutions of Elliptic Partial Differential Equations or Inequalities (J. Math. pures et appl., T. 36, (1957, pp. 235-249). | MR 19,1056c | Zbl 0084.30402

[2] L. Bers, F. John and M. Schechter, Partial Differential Equations, Interscience, New York, 1964. | MR 29 #346 | Zbl 0126.00207

[3] S. Bochner, Harmonic Surfaces in Riemannian Metric (Trans. Amer. Math. Soc., Vol. 47, 1940 pp. 146-154). | JFM 66.0483.05 | MR 1,271d | Zbl 0022.39703

[4] S. Bochner, Curvature in Hermitian Metric (Bull. Amer. Math. Soc., Vol. 53, 1947, pp. 179-195). | MR 8,490d | Zbl 0035.10403

[5] S. Bochner, Curvature and Betti Numbers (Ann. Math., Vol. 49, 1948, pp. 379-390). | MR 9,618d | Zbl 0038.34401

[6] A. Borel, Les fonctions automorphes de plusieurs variables complexes (Bull. Soc. Math., T. 80, 1952, pp. 167-182). | Numdam | MR 14,1077a | Zbl 0048.06401

[7] C. Earle and J. Eells Jr., A Fiber Bundle Description of Teichmüller Theory (Compos. Math., Vol. 21, 1969, pp. 155-161).

[8] J. Eells Jr. and L. Lemaire, A Report on Harmonic Maps (to appear in the Bull. London Math. Soc.). | Zbl 0401.58003

[9] J. Eells Jr. and J. H. Sampson, Harmonic Mappings of Riemannian Manifolds (Amer. J. Math., Vol. 86, 1964, pp. 109-160). | MR 29 #1603 | Zbl 0122.40102

[10] J. Eells Jr. and J. C. Wood, Restrictions on Harmonic Maps of Surfaces (Topology, Vol. 15, 1976, 263-266). | MR 54 #8720 | Zbl 0328.58008

[11] L. P. Eisenhart, Riemannian Geometry, Princeton, 1949. | MR 11,687g | Zbl 0041.29403

[12] A. Friedman, Partial Differential Equations of Parabolic Type, Prentice-Hall, Englewood Cliffs, N. H., 1964. | MR 31 #6062 | Zbl 0144.34903

[13] A. Friedman, Interior Estimates for Parabolic Systems of Partial Differential Equations (J. Maths. and Mech., Vol. 7, 1958, pp. 393-418). | MR 21 #7362 | Zbl 0082.30402

[13 a] M. Gerstenhaber and H. E. Rauch, On Extremal quasi-conformal Mappings. I and II (Proc. Nat. Acad. Sc., Vol. 40, 1954, pp. 808-816 and 991-994). | MR 16,349a | Zbl 0056.07502

[14] R. S. Hamilton, Harmonic Mappings of Manifolds with Boundary (Springer Lecture Notes in Mathematics, No. 471, 1975, New York). | MR 58 #2872 | Zbl 0308.35003

[15] P. Hartman, On Homotopic Harmonic Maps (Can. J. Math., Vol. 19, 1967, pp. 673-687). | MR 35 #4856 | Zbl 0148.42404

[16] E. Heinz, Über gewisse elliptische Systeme von Differentialgleichungen zweiter Ordnung mit Anwendung auf die Monge-Ampèresche Gleichung (Math. Ann., Vol. 131, 1956, pp. 411-428). | MR 23 #A1131 | Zbl 0072.31103

[17] S. Helgason, Differential Geometry and Symmetric Spaces. Academic Press, New York, 1962. | MR 26 #2986 | Zbl 0111.18101

[18] A. Hurwitz, Über algebraische Gebilde u. s. w., Gesammelte Abhandlungen.

[19] J. Kazdan and F. W. Warner, Curvature Functions for Compact 2-manifolds (Ann. Math., Vol. 99, 1974, pp. 14-47). | MR 49 #7949 | Zbl 0273.53034

[20] S. Kobayashi, Intrinsic Distances, Measures and Geometric Theory (Bull. Amer. Math. Soc., Vol. 82, 1976, pp. 357-416). | MR 54 #3032 | Zbl 0346.32031

[21] S. Lang, Integral Points on Curves (Publ. Math., No. 6, I.H.E.S., Paris, 1960, pp. 27-43). | Numdam | MR 24 #A86 | Zbl 0112.13402

[21 a] S. Lang, Some Theorems and Conjectures in Diophantine Equations (Bull. Amer. Math. Soc., Vol. 66, 1960, pp. 240-249). | MR 22 #9469 | Zbl 0095.26301

[22] M. Lees and M. H. Protter, Unique Continuation for Parabolic Differential Equations and Inequalities (Duke Math. J., Vol. 28, 1961, pp. 369-382). | MR 25 #4254 | Zbl 0143.33301

[23] L. Nirenberg, A Strong Maximum Principle for Parabolic Equations (Comm. Pure and Appl. Maths., Vol. 6, 1953, pp. 167-177). | MR 14,1089e | Zbl 0050.09601

[23 a] O. Nouhaud, Déformations infinitésimales harmoniques (C. R. Acad. Sc., T. 275, série A, 1972, pp. 999-1001 and 1103-1106). | MR 57 #4025a | Zbl 0243.53022

[24] H. E. Rauch, On the Transcendental Moduli of Algebraic Riemann Surfaces (Proc. Nat. Acad. Sc., Vol. 41, 1965, pp. 42-49, 176-180 and 231-238). | MR 17,251e | Zbl 0067.30502

[25] R. Schoen and S. T. Yau, Univalent Harmonic Maps of Surfaces [Invent. Math. (to appear)].

[26] J. H. Sampson, A Note on Automorphic Functions (Proc. Nat. Acad. Sc., Vol. 38, 1952, pp. 895-898). | MR 14,633c | Zbl 0048.06402

[27] K. Shibata, On the Existence of a Harmonic Mapping (Osaka Math. J., Vol. 15, 1963, pp. 173-211). | MR 28 #1289 | Zbl 0132.06004

[28] R. T. Smith, Harmonic Mappings of Spheres (Dissertation, Warwick University, 1972).

[29] J. C. Wood, Singularities of Harmonic Maps and Applications of the Gauss-Bonnet Formula [Amer. J. Math. (to appear, at last)]. | Zbl 0375.35022

[30] J. C. Wood, Harmonic Maps and Complex Analysis (Proc. of a Summer Course in Complex Analysis, Vol. III, Trieste, 1975, pp. 289-308). | MR 58 #31207 | Zbl 0346.53030