References
Abraham R 1962Lectures of Smale on differential topology. Columbia University
Abraham R 1970 Bumpy metrics;Proc. Symp. Pure. Math. 14 1–3
Abraham R and Robbin J 1967Transversal mappings and flows (New York: Benjamin)
Calabi E 1969 An intrinsic characterisation of harmonic one-forms;Global Analysis (Papers in honour of K Kodaira) (Princeton: University Press and 1969 University of Tokyo Press) 101–117
Dieudonne J A 1960Foundations of modern analysis (New York: Academic Press)
Earle C J and Eells J 1969 A fibre bundle description of Teichmüller theory;J. Diff. Geom. 3 19–43
Edmonds A L 1980 Deformations of maps to branched coverings in dimension two (to appear)
Eells J 1966 A setting for global analysis;Bull. Am. Math. Soc. 72 751–807
Eells J and Lemaire L 1978 A report on harmonic maps;Bull. London Math. Soc. 10 1–68
Eells J and Sampson J H 1964 Harmonic mappings of Riemannian manifolds;Am. J. Math. 86 109–160
Eells J and Wood J C 1976 Restrictions on harmonic maps of surfaces;Topology 15 263–266
Gilbarg D and Trudinger N S 1977Elliptic partial differential equations of second order (Grundlehren 224: Springer Verlag)
Goldstein R A 1972 Stability of the boundary value problem for harmonic mappings;J. Math. Anal. Appl. 39 346–359
Hamilton R S 1975Harmonic maps of manifolds with boundary. Springer lecture notes 471
Hartman P 1967 On homotopic harmonic maps;Can. J. Math. 19 673–687
Hōrmander L 1964Linear partial differential operators (Grundlehren: Springer Verlag)
Lemaire L 1975 Applications harmoniques de surfaces;CR Acad. Sci. Paris A 280 897–899
Lemaire L 1978 Harmonic nonholomorphic maps from a surface to a sphere;Proc. Am. Math. Soc. 71 299–304
Lichnerowicz A 1961 Propagateurs et commutateurs en relativite generale;IHES Publ. 10
Mazet E 1973 La formule de la variation seconde de l'energie au voisinage d'une application harmonique;J. Diff. Geom. 8 279–296
Morrey C B 1966Multiple integrals in the calculus of variations. (Grundlehren: Springer Verlag)
Morse M 1934 The calculus of variations in the large;Am. Math. Soc. Colloq. Publ. 18
Royden H L 1960 The analytic approximation of differentiable mappings;Math. Ann. 139 171–179
Sampson J H 1978 Some properties and applications of harmonic mappings;Ann. Ec. Norm. Sup. 11 221–228
Schoen R M 1977Existence and regularity of some geometric variational problems; Thesis, Stanford Univ.
Schoen R M and Yau S T 1978 On univalent harmonic maps between surfaces;Invent. Math. 44 265–278
Siegel C L and Moser J K 1971Lectures on classical mechanics (Grundlehren: Springer Verlag)
Smith R T 1975 Harmonic mappings of spheres;Am. J. Math. 97 364–385
Smith R T 1975 The second variation formula for harmonic mappings;Proc. Am. Math. Soc. 47 229–236
Visik M I 1951 On strongly elliptic systems of differential equations;Math. Sbornik 29 615–676
Whitney H 1934 Analytic extension of differentiable functions defined on closed sets;Trans. Am. Math. Soc. 36 63–89
Wood J C 1977 Singularities of harmonic maps and applications of the Gauss-Bonne formula;Am. J. Math. 99 1329–1344
Author information
Authors and Affiliations
Additional information
During the preparation of this paper the authors enjoyed the hospitality of the Institut des Hautes Etudes Scientifiques. The first-named thanks the Université de Paris VI, where he was Professeur d'Echange. The second-named is Chargé de recherches au Fonds National Belge de la Recherche Scientifique.
Rights and permissions
About this article
Cite this article
Eells, J., Lemaire, L. Deformations of metrics and associated harmonic maps. Proc Math Sci 90, 33–45 (1981). https://doi.org/10.1007/BF02867016
Issue Date:
DOI: https://doi.org/10.1007/BF02867016