Energy estimates and Liouville theorems for harmonic maps
Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 23 (1990) no. 4, pp. 563-592.
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     author = {Takegoshi, Kensh\^o},
     title = {Energy estimates and {Liouville} theorems for harmonic maps},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {563--592},
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     language = {en},
     url = {http://www.numdam.org/articles/10.24033/asens.1613/}
}
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Takegoshi, Kenshô. Energy estimates and Liouville theorems for harmonic maps. Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 23 (1990) no. 4, pp. 563-592. doi : 10.24033/asens.1613. http://www.numdam.org/articles/10.24033/asens.1613/

[1] E. Bedford, B. A. Taylor, Two applications of a non-linear integral formula to analytic functions (Indiana Univ. Math. J., Vol. 29, 1980, pp. 463-465). | MR | Zbl

[2] S. Y. Cheng, Liouville theorem for harmonic maps, Geometry of the Laplace operator (Proc. Sym. Pure Math., Vol. 36, 1980, pp. 147-151). | MR | Zbl

[3] S. Y. Cheng, S. T. Yau, Differential equations on Riemannian manifolds and their geometric applications (Comm. Oure Appl. Math., Vol. 28, 1975, pp. 333-354). | MR | Zbl

[4] H. Donnelly, Bounded harmonic functions and positive Ricci curvature (Math. Z., Vol. 191, 1986, pp. 559-565). | MR | Zbl

[5] H. Donnelly, C. Fefferman, L² cohomology and index theorem for the Gergman metric (Ann. Math., Vol. 118, 1983, pp. 593-618). | MR | Zbl

[6] H. Donnelly, F. Xavier, On the differential form spectrum of negatively curved Riemannian manifolds (Am. J. Math., Vol. 106, 1984, pp. 169-185). | MR | Zbl

[7] J. Eells, L. Lemaire, A report on harmonic maps (Bull. London Math. Soc., Vol. 10, 1978, pp. 1-68). | MR | Zbl

[8] R. E. Greene, H. Wu, Integral of subharmonic functions on manifolds of non-negative curvature (Invent. Math., Vol. 27, 1974, pp. 265-298). | MR | Zbl

[9] R. E. Greene, H. Wu, Function theory on manifolds which possesses a pole (Lect. Notes Math., Vol. 699, 1979, Springer Verlag). | MR | Zbl

[10] W. K. Hayman, Meromorphic functions, Clarendon Press, Oxford, 1964. | MR | Zbl

[11] S. Hildebrandt, Liouville theorems for harmonic mappings and application to Bernstein theorems, Seminor on differential geometry (Ann. Math. Studies, Vol. 102, 1982, pp. 107-131). | MR | Zbl

[12] H. Kaneko, A stochastic approach to Liouville property for plurisubharmonic functions (J. Math. Soc., Vol. 41, 1989, pp. 291-299). | MR | Zbl

[13] L. Karp, Subharmonic functions on real and complex manifolds (Math. Z., vol. 179, 1982, pp. 534-554). | MR | Zbl

[14] A. Kasue, On Riemannian manifolds admitting certain strictly convex function (Osaka J. Math., Vol. 18, 1981, pp. 577-582). | MR | Zbl

[15] A. Kasue, K. Sugawara, Gap theorems for certain submanifolds of Euclidean spaces and hyperbolic space forms (Osaka J. Math., Vol. 24, 1987, pp. 679-704). | MR | Zbl

[16] P. Li and L. F. Tam, Positive harmonic functions on complete manifolds with non-negative curvature outside a compact set (Ann. Math., Vol. 125, 1987, pp. 171-207). | MR | Zbl

[17] N. Mok, Y. T. Siu and S. T. Yau, The Poincaré-Lelong equation on complete Kähler manifolds (Comp. Math., Vol. 44, 1981, pp. 183-218). | Numdam | MR | Zbl

[18] J. Moser, On Harnack's theorem for elliptic differential equations (Comm. Pure Appl. Math., Vol. 14, 1961, pp. 577-591). | MR | Zbl

[19] P. Price, A monotonicity formula for Yang-Mills firleds (Manuscripta Math., Vol. 43, 1983, pp. 131-166). | MR | Zbl

[20] J. H. Sampson, Some properties and applications of harmonic mappings (Ann. Scient. Éc. Norm. Sup., Vol. 11, 1978, pp. 211-228). | Numdam | MR | Zbl

[21] B. V. Schabat, Distribution of values of holomorphic mappings, Translation of Mathematical Monographs (Am. Math. Soc., Vol. 61, 1985). | Zbl

[22] N. Sibony and P. M. Wong, Some remarks on the Casorati-Weierstrass theorem (Ann. Polonici Math., Vol. 39, 1981, pp. 165-174). | MR | Zbl

[23] Y. T. Siu, The complex analyticity of harmonic maps and the strong rigidity of compact Kähler manifolds (Ann. Math., Vol. 112, 1980, pp. 73-111). | MR | Zbl

[24] Y. T. Siu, Complex analyticity of harmonic maps, vanishing and Lefschetz theorems (J. Diff. Geometry, Vol. 17, 1982, pp. 55-138). | MR | Zbl

[25] Y. T. Siu, S. T. Yau, Complete Kähler manifolds with non-positive curvature of faster than quadratic decay (Ann. Math., Vol. 105, 1977, pp. 225-264). | MR | Zbl

[26] W. Stoll, The growth of area of a transcendental analytic set I, II (Math. Ann., Vol. 156, 1964, pp. 47-78 ; pp. 144-170). | MR | Zbl

[27] W. Stoll, Value distribution on parabolic spaces (Lect. Notes Math., Vol. 600, 1977, Springer Verlag). | MR | Zbl

[28] K. Takegoshi, A non-existence theorem for pluriharmonic maps of finite energy (Math. Z., Vol. 192, 1986, pp. 21-27). | MR | Zbl

[29] A. Vitter, On the curvature of complex hypersurfaces (Indiana Univ. Math. J., Vol. 23, 1974, pp. 813-826). | MR | Zbl

[30] H. Wu, On a problem concerning the intrinsic characterization of ℂn (Math. Ann., Vol. 246, 1979, pp. 15-22). | MR | Zbl

[31] H. Wu, The Bochner technique in differential geometry, Mathematical Report Series, Harwoord Academic Press, 1987.

[32] S. T. Yau, Harmonic functions on complete Riemannian manifolds (Comm. Pure Appl. Math., Vol. 28, 1975, pp. 201-228). | MR | Zbl

[33] S. T. Yau, A general Schwarz lemma for Kähler Manifolds (Am. J. Math., Vol. 100, 1978, pp. 197-204). | MR | Zbl

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