Some properties and applications of harmonic mappings
Annales scientifiques de l'École Normale Supérieure (1978)
- Volume: 11, Issue: 2, page 211-228
- ISSN: 0012-9593
Access Full Article
topHow to cite
topSampson, J. H.. "Some properties and applications of harmonic mappings." Annales scientifiques de l'École Normale Supérieure 11.2 (1978): 211-228. <http://eudml.org/doc/82013>.
@article{Sampson1978,
author = {Sampson, J. H.},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {Moduli of Riemann Surfaces; Unique Continuation Properties of Harmonic Mappings; Holomorphic Quadratic Differential; Aronszajn-Carleman Theorem; Maximum Principle; Geodesic Submanifolds; Harmonic Immersions; Conformal Metric on a Compact Riemann Surface; Smooth Deformations; Automorphic Varieties},
language = {eng},
number = {2},
pages = {211-228},
publisher = {Elsevier},
title = {Some properties and applications of harmonic mappings},
url = {http://eudml.org/doc/82013},
volume = {11},
year = {1978},
}
TY - JOUR
AU - Sampson, J. H.
TI - Some properties and applications of harmonic mappings
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1978
PB - Elsevier
VL - 11
IS - 2
SP - 211
EP - 228
LA - eng
KW - Moduli of Riemann Surfaces; Unique Continuation Properties of Harmonic Mappings; Holomorphic Quadratic Differential; Aronszajn-Carleman Theorem; Maximum Principle; Geodesic Submanifolds; Harmonic Immersions; Conformal Metric on a Compact Riemann Surface; Smooth Deformations; Automorphic Varieties
UR - http://eudml.org/doc/82013
ER -
References
top- [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). Zbl0084.30402MR19,1056c
- [2] L. BERS, F. JOHN and M. SCHECHTER, Partial Differential Equations, Interscience, New York, 1964. Zbl0126.00207MR29 #346
- [3] S. BOCHNER, Harmonic Surfaces in Riemannian Metric (Trans. Amer. Math. Soc., Vol. 47, 1940 pp. 146-154). Zbl0022.39703MR1,271dJFM66.0483.05
- [4] S. BOCHNER, Curvature in Hermitian Metric (Bull. Amer. Math. Soc., Vol. 53, 1947, pp. 179-195). Zbl0035.10403MR8,490d
- [5] S. BOCHNER, Curvature and Betti Numbers (Ann. Math., Vol. 49, 1948, pp. 379-390). Zbl0038.34401MR9,618d
- [6] A. BOREL, Les fonctions automorphes de plusieurs variables complexes (Bull. Soc. Math., T. 80, 1952, pp. 167-182). Zbl0048.06401MR14,1077a
- [7] C. EARLE and J. EELLS Jr., A Fiber Bundle Description of Teichmüller Theory (Compos. Math., Vol. 21, 1969, pp. 155-161). Zbl0185.32901
- [8] J. EELLS Jr. and L. LEMAIRE, A Report on Harmonic Maps (to appear in the Bull. London Math. Soc.). Zbl0401.58003
- [9] J. EELLS Jr. and J. H. SAMPSON, Harmonic Mappings of Riemannian Manifolds (Amer. J. Math., Vol. 86, 1964, pp. 109-160). Zbl0122.40102MR29 #1603
- [10] J. EELLS Jr. and J. C. WOOD, Restrictions on Harmonic Maps of Surfaces (Topology, Vol. 15, 1976, 263-266). Zbl0328.58008MR54 #8720
- [11] L. P. EISENHART, Riemannian Geometry, Princeton, 1949. Zbl0041.29403MR11,687g
- [12] A. FRIEDMAN, Partial Differential Equations of Parabolic Type, Prentice-Hall, Englewood Cliffs, N. H., 1964. Zbl0144.34903MR31 #6062
- [13] A. FRIEDMAN, Interior Estimates for Parabolic Systems of Partial Differential Equations (J. Maths. and Mech., Vol. 7, 1958, pp. 393-418). Zbl0082.30402MR21 #7362
- [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). Zbl0056.07502MR16,349a
- [14] R. S. HAMILTON, Harmonic Mappings of Manifolds with Boundary (Springer Lecture Notes in Mathematics, No. 471, 1975, New York). Zbl0308.35003MR58 #2872
- [15] P. HARTMAN, On Homotopic Harmonic Maps (Can. J. Math., Vol. 19, 1967, pp. 673-687). Zbl0148.42404MR35 #4856
- [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). Zbl0072.31103MR23 #A1131
- [17] S. HELGASON, Differential Geometry and Symmetric Spaces. Academic Press, New York, 1962. Zbl0111.18101MR26 #2986
- [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). Zbl0273.53034MR49 #7949
- [20] S. KOBAYASHI, Intrinsic Distances, Measures and Geometric Theory (Bull. Amer. Math. Soc., Vol. 82, 1976, pp. 357-416). Zbl0346.32031MR54 #3032
- [21] S. LANG, Integral Points on Curves (Publ. Math., No. 6, I.H.E.S., Paris, 1960, pp. 27-43). Zbl0112.13402MR24 #A86
- [21 a] S. LANG, Some Theorems and Conjectures in Diophantine Equations (Bull. Amer. Math. Soc., Vol. 66, 1960, pp. 240-249). Zbl0095.26301MR22 #9469
- [22] M. LEES and M. H. PROTTER, Unique Continuation for Parabolic Differential Equations and Inequalities (Duke Math. J., Vol. 28, 1961, pp. 369-382). Zbl0143.33301MR25 #4254
- [23] L. NIRENBERG, A Strong Maximum Principle for Parabolic Equations (Comm. Pure and Appl. Maths., Vol. 6, 1953, pp. 167-177). Zbl0050.09601MR14,1089e
- [23 a] O. NOUHAUD, Déformations infinitésimales harmoniques (C. R. Acad. Sc., T. 275, série A, 1972, pp. 999-1001 and 1103-1106). Zbl0243.53022MR57 #4025a
- [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). Zbl0067.30502MR17,251e
- [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). Zbl0048.06402MR14,633c
- [27] K. SHIBATA, On the Existence of a Harmonic Mapping (Osaka Math. J., Vol. 15, 1963, pp. 173-211). Zbl0132.06004MR28 #1289
- [28] R. T. SMITH, Harmonic Mappings of Spheres (Dissertation, Warwick University, 1972). Zbl0279.53055
- [29] J. C. WOOD, Singularities of Harmonic Maps and Applications of the Gauss-Bonnet Formula [Amer. J. Math. (to appear, at last)]. Zbl0375.35022
- [30] J. C. WOOD, Harmonic Maps and Complex Analysis (Proc. of a Summer Course in Complex Analysis, Vol. III, Trieste, 1975, pp. 289-308). Zbl0346.53030MR58 #31207
Citations in EuDML Documents
top- Mohamed Tahar Kadaoui Abbassi, Giovanni Calvaruso, Domenico Perrone, Some examples of harmonic maps for -natural metrics
- Luc Lemaire, Existence des applications harmoniques et courbure des variétés
- James A. Carlson, Domingo Toledo, Harmonic mappings of Kähler manifolds to locally symmetric spaces
- Kenshô Takegoshi, Energy estimates and Liouville theorems for harmonic maps
- Vincent Koziarz, Julien Maubon, Harmonic maps and representations of non-uniform lattices of
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.