@article{ASENS_1990_4_23_4_563_0, 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}, publisher = {Elsevier}, volume = {Ser. 4, 23}, number = {4}, year = {1990}, doi = {10.24033/asens.1613}, mrnumber = {91j:58047}, zbl = {0718.58018}, language = {en}, url = {http://archive.numdam.org/articles/10.24033/asens.1613/} }
TY - JOUR AU - Takegoshi, Kenshô TI - Energy estimates and Liouville theorems for harmonic maps JO - Annales scientifiques de l'École Normale Supérieure PY - 1990 SP - 563 EP - 592 VL - 23 IS - 4 PB - Elsevier UR - http://archive.numdam.org/articles/10.24033/asens.1613/ DO - 10.24033/asens.1613 LA - en ID - ASENS_1990_4_23_4_563_0 ER -
%0 Journal Article %A Takegoshi, Kenshô %T Energy estimates and Liouville theorems for harmonic maps %J Annales scientifiques de l'École Normale Supérieure %D 1990 %P 563-592 %V 23 %N 4 %I Elsevier %U http://archive.numdam.org/articles/10.24033/asens.1613/ %R 10.24033/asens.1613 %G en %F ASENS_1990_4_23_4_563_0
Takegoshi, Kenshô. Energy estimates and Liouville theorems for harmonic maps. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 23 (1990) no. 4, pp. 563-592. doi : 10.24033/asens.1613. http://archive.numdam.org/articles/10.24033/asens.1613/
[1] Two applications of a non-linear integral formula to analytic functions (Indiana Univ. Math. J., Vol. 29, 1980, pp. 463-465). | MR | Zbl
, ,[2] Liouville theorem for harmonic maps, Geometry of the Laplace operator (Proc. Sym. Pure Math., Vol. 36, 1980, pp. 147-151). | MR | Zbl
,[3] Differential equations on Riemannian manifolds and their geometric applications (Comm. Oure Appl. Math., Vol. 28, 1975, pp. 333-354). | MR | Zbl
, ,[4] Bounded harmonic functions and positive Ricci curvature (Math. Z., Vol. 191, 1986, pp. 559-565). | MR | Zbl
,[5] L² cohomology and index theorem for the Gergman metric (Ann. Math., Vol. 118, 1983, pp. 593-618). | MR | Zbl
, ,[6] On the differential form spectrum of negatively curved Riemannian manifolds (Am. J. Math., Vol. 106, 1984, pp. 169-185). | MR | Zbl
, ,[7] A report on harmonic maps (Bull. London Math. Soc., Vol. 10, 1978, pp. 1-68). | MR | Zbl
, ,[8] Integral of subharmonic functions on manifolds of non-negative curvature (Invent. Math., Vol. 27, 1974, pp. 265-298). | MR | Zbl
, ,[9] Function theory on manifolds which possesses a pole (Lect. Notes Math., Vol. 699, 1979, Springer Verlag). | MR | Zbl
, ,[10] Meromorphic functions, Clarendon Press, Oxford, 1964. | MR | Zbl
,[11] 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] A stochastic approach to Liouville property for plurisubharmonic functions (J. Math. Soc., Vol. 41, 1989, pp. 291-299). | MR | Zbl
,[13] Subharmonic functions on real and complex manifolds (Math. Z., vol. 179, 1982, pp. 534-554). | MR | Zbl
,[14] On Riemannian manifolds admitting certain strictly convex function (Osaka J. Math., Vol. 18, 1981, pp. 577-582). | MR | Zbl
,[15] Gap theorems for certain submanifolds of Euclidean spaces and hyperbolic space forms (Osaka J. Math., Vol. 24, 1987, pp. 679-704). | MR | Zbl
, ,[16] Positive harmonic functions on complete manifolds with non-negative curvature outside a compact set (Ann. Math., Vol. 125, 1987, pp. 171-207). | MR | Zbl
and ,[17] The Poincaré-Lelong equation on complete Kähler manifolds (Comp. Math., Vol. 44, 1981, pp. 183-218). | Numdam | MR | Zbl
, and ,[18] On Harnack's theorem for elliptic differential equations (Comm. Pure Appl. Math., Vol. 14, 1961, pp. 577-591). | MR | Zbl
,[19] A monotonicity formula for Yang-Mills firleds (Manuscripta Math., Vol. 43, 1983, pp. 131-166). | MR | Zbl
,[20] Some properties and applications of harmonic mappings (Ann. Scient. Éc. Norm. Sup., Vol. 11, 1978, pp. 211-228). | Numdam | MR | Zbl
,[21] Distribution of values of holomorphic mappings, Translation of Mathematical Monographs (Am. Math. Soc., Vol. 61, 1985). | Zbl
,[22] Some remarks on the Casorati-Weierstrass theorem (Ann. Polonici Math., Vol. 39, 1981, pp. 165-174). | MR | Zbl
and ,[23] 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] Complex analyticity of harmonic maps, vanishing and Lefschetz theorems (J. Diff. Geometry, Vol. 17, 1982, pp. 55-138). | MR | Zbl
,[25] Complete Kähler manifolds with non-positive curvature of faster than quadratic decay (Ann. Math., Vol. 105, 1977, pp. 225-264). | MR | Zbl
, ,[26] 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] Value distribution on parabolic spaces (Lect. Notes Math., Vol. 600, 1977, Springer Verlag). | MR | Zbl
,[28] A non-existence theorem for pluriharmonic maps of finite energy (Math. Z., Vol. 192, 1986, pp. 21-27). | MR | Zbl
,[29] On the curvature of complex hypersurfaces (Indiana Univ. Math. J., Vol. 23, 1974, pp. 813-826). | MR | Zbl
,[30] On a problem concerning the intrinsic characterization of ℂn (Math. Ann., Vol. 246, 1979, pp. 15-22). | MR | Zbl
,[31] The Bochner technique in differential geometry, Mathematical Report Series, Harwoord Academic Press, 1987.
,[32] Harmonic functions on complete Riemannian manifolds (Comm. Pure Appl. Math., Vol. 28, 1975, pp. 201-228). | MR | Zbl
,[33] A general Schwarz lemma for Kähler Manifolds (Am. J. Math., Vol. 100, 1978, pp. 197-204). | MR | Zbl
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