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References
Al'ber, S. I., On n-dimensional problems in the calculus of variation in the large, Sov. Math. Dokl. 5, 700–794 (1964).
Al'ber, S. I., Spaces of mappings into a manifold with negative curvature, Sov. Math. Dokl. 9, 6–9 (1967).
Arakelov, S. J., Families of algebraic curves with fixed degeneracies, Math. USSR Izv. 5, 1277–1302 (1971).
Carlson, J., and D. Toledo, Harmonic mappings of Kähler manifolds to locally symmetric spaces, Publ. Math. IHES, to appear.
Corlette, K., Flat G-bundles with canonical metrics, J. Diff. Geom. 28, 361–382 (1988).
Diederich, K., and T. Ohsawa, Harmonic mappings and disk bundles over compact Kähler manifolds
Donaldson, S., Twisted harmonic maps and the self-duality equations, Proc. London Math. Soc. 55, 127–131 (1987).
Eells, J., and L. Lemaire, Another report on harmonic maps, Bull. London Math. Soc. 20, 385–524 (1988).
Eells, J., and J. Sampson, Harmonic mappings of Riemannian manifolds, Amer. J. Math. 85, 109–160 (1964).
Faltings, G., Arakelov's theorem for Abelian varieties, Inv. Math. 73, 337–347 (1983).
Grauert, H., Mordells Vermutung über rationale Punkte auf algebraischen Kurven und Funktionenkörper, Publ. Math. IHES 25, 363–381 (1965).
Grauert, H., and H. Reckziegel, Hermitesche Metriken und normale Familien holomorpher Abbildungen, Math. Z. 89, 108–125 (1965).
Griffiths, P., periods of integrals on algebraic manifolds: Summary of main results and discussion of open problems, Bull. AMS 76, 228–296 (1970).
Hartman, P., On homotopic harmonic maps, Can. J. Math. 19, 673–687 (1967).
Hildebrandt, S., H. Kaul, and K.-O. Widman, An existence theorem for harmonic mappings of Riemannian manifolds, Acta Math. 138, 1–16 (1977).
Imayoshi, Y., and H. Shiga, A finiteness theorem for holomorphic families of Riemann surfaces, in: Holomorphic functions and moduli II, pp. 207–220, ed. by D. Drasin, et al., Springer, 1988.
Jost, J., Harmonic mappings between Riemannian manifolds, Proc. CMA Vol. 4, ANU-Press, Canberra, 1984.
Jost, J., Nonlinear methods in Riemannian and Kählerian geometry, Birkhauser, Basel, Boston, 1988.
Jost, J., Two dimensional geometric variational problems, Wiley-Interscience, to appear.
Jost, J., and S.-T. Yau, Harmonic mappings and Kähler manifolds, Math. Ann. 262, 145–166 (1983).
Jost, J., and S.-T. Yau, A strong rigidity theorem for a certain class of compact analytic surfaces, Math. Ann. 271, 143–152 (1985).
Jost, J., and S.-T. Yau, The strong rigidity of locally symmetric complex manifolds of rank one and finite volume, Math. Ann. 275, 291–304 (1986).
Jost, J., and S.-T. Yau, On the rigidity of certain discrete groups and algebraic varieties, Math. Ann. 278, 481–496 (1987).
Jost, J., and S.-T. Yau, Harmonic maps and group representations, to appear in volume in honor of M. doCarmo (B. Lawson, ed.).
Jost, J., and S.-T. Yau, Harmonic mappings and algebraic varieties over function fields, preprint.
Kobayashi, S., and K. Nomizu, Foundations of differential geometry, Vol. 1, Wiley, New York, 1963.
Labourie, F., Existence d'applications harmoniques tordues à valeurs dans les variéteé à courbure négative, preprint.
Manin, Ju. I., Rational points of algebraic curves over function fields, Amer. Math. Soc. Transl. 50, 189–234 (1966).
Margulis, G. A., Discrete groups of motion of manifolds of nonpositive curvature, AMS Transl. 190, 33–45 (1977).
Margulis, G. A., Discrete subgroups of Lie groups, monograph, to appear.
Mok, N., The holomorphic or antiholomorphic character of harmonic maps into irreducible compact quotients of polydiscs, Math. Ann. 272, 197–216 (1985).
Mok, N., Uniqueness theorems of Hermitian metrics of seminegative curvature on quotients of bounded symmetric domains, Ann. Math. 125, 105–152 (1987).
Mok, N., Strong rigidity of irreducible quotients of polydiscs of finite volume, Math. Ann. 282, 555–578 (1988).
Mostow, G., Strong rigidity of locally symmetric spaces, Ann. Math. Studies 78, Princeton, 1973.
Noguchi, J., Moduli spaces of holomorphic mappings into hyperbolically imbedded complex spaces and locally symmetric spaces, Inv. math. 93, 15–34 (1988).
Parshin, A. N., Algebraic curves over function fields, I., Math. USSR Izv. 2, 1145–1170 (1968).
Prasad, G., Strong rigidity of Q-rank 1 lattices, Inv. math. 21, 255–286 (1973).
Royden, H., The Ahlfors-Schwarz lemma in several complex variables, Comment. Math. Helv. 55, 547–558 (1980).
Sacks, J., and K. Uhlenbeck, The existence of minimal immersions of 2-spheres, Ann. Math. 113, 1–24 (1981).
Sampson, J., Applications of harmonic maps to Kähler geometry, Contemp. Math. 49, 125–134 (1986).
Schumacher, G., Harmonic maps of the moduli space of compact Riemann surfaces, Math. Ann. 275, 455–466 (1986).
Shiga, Lecture at the Taniguchi Symposium, Katata, August 1989.
Siu, Y.-T., The complex analyticity of harmonic maps and the strong rigidity of compact Kähler manifolds, Ann. Math. 112, 73–111 (1980).
Siu, Y.-T., Complex analyticity of harmonic maps, vanishing, and Lefschetz theorems, J. Diff. Geom. 17, 555–138 (1982).
Siu, Y.-T., Strong rigidity for Kähler manifolds and the construction of bounded holomorphic functions, pp. 124–151, in: R. Howe (ed.), Discrete groups in geometry and analysis, Birkhauser, Boston, Basel, 1987.
Spatzier, and R. Zimmer, Fundamental groups of negatively curved manifolds and actions of semisimple groups, Preprint.
Tromba, A., On a natural affine connection on the space of almost complex structures and the curvature of Teichmüller space with respect to its Weil-Petersson metric, Man. Math. 56, 475–497 (1986).
Wolpert, S., Chern forms and the Riemann tensor for the moduli space of curves, Inv. Math. 85, 119–145 (1986).
Wolpert, S., Geodesic length functions and the Nielsen problem, J. Diff. Geom. 25, 275–296 (1987).
Yau, S.-T., A general Schwarz lemma for Kähler manifolds, Amer. J. Math. 100, 197–203 (1978).
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Jost, J., Yau, ST. (1991). Harmonic maps and Kähler geometry. In: Noguchi, J., Ohsawa, T. (eds) Prospects in Complex Geometry. Lecture Notes in Mathematics, vol 1468. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0086200
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DOI: https://doi.org/10.1007/BFb0086200
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