A Liouville theorem on an analytic space

Kensho TAKEGOSHI

doi:10.2969/jmsj/04520301

Kensho TAKEGOSHI

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JOURNAL FREE ACCESS

1993 Volume 45 Issue 2 Pages 301-311

DOI https://doi.org/10.2969/jmsj/04520301

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Published: 1993 Received: June 17, 1991 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : FI) G. Fischer, Complex analytic geometry, Lecture Notes in Math., 538, Springer, Berlin-Heidelberg-New York, 1976.
GR) H. Grauert, Bemerkenswerte pseudokonvexe Mannigfaltigkeiten, Math. Z., 81 (1963), 377-391.
GUR) R. C. Gunning and H. Rossi, Analytic functions of several complex variables, Prentice-Hall, 1965.
GW1) R.E. Greene and H. Wu, Integrals of subharmonic functions on manifolds of nonnegative curvature, Invent. Math., 27 (1974), 265-298.
GW2) R. E. Greene and H. Wu, Function theory on manifolds which possesses a pole, Lecture Notes in Math., 699, Springer, Berlin-Heidelberg-New York, 1979.
KA1) H. Kaneko, A stochastic approach to a Liouville property for plurisubharmonic functions, J. Math. Soc. Japan, 41 (1989), 291-299.
KA2) H. Kaneko, Private communication.
NO) J. Noguchi and T. Ochiai, Geometric function theory in several complex variables, Transl. Math. Monographs, 80, Amer. Math. Soc., 1990.
RI) R. Richberg, Stetige streng pseudokonvexe Funktionen, Math. Ann., 175 (1968), 257-286.
SIW) N. Sibony and P. M. Wong, Some remarks on the Casorati-Weierstrass' theorem, Ann. Polon. Math., 39 (1981), 165-174.
ST1) W. Stoll, The growth of area of a transcendental analytic set I, II, Math. Ann., 156 (1964), 47-78, 144-170.
ST2) W. Stoll, The Ahlfors-Weyl theory of meromorphic maps on parabolic manifolds, Lecture Notes in Math., 981, Springer, Berlin-Heidelberg-New York-Tokyo, 1983, pp. 101-219.
TA1) K. Takegoshi, A non-existence theorem for pluriharmonic maps of finite energy, Math. Z., 192 (1986), 21-27.
TA2) K. Takegoshi, Energy estimates and Liouville theorems for harmonic maps, Ann. Sci. École Norm. Sup., 23 (1990), 563-592.
TU) Ch. Tung, The first main theorem of value distribution on complex spaces, Atti Acad. Naz. Lincei Mem. Cl. Sci. Fis. Mat. Natur. Sez. Ia (8), 15 (1979), 91-263.
WU1) H. Wu, Remarks on the first main theorem in equidistribution theory, I, II, III, IV, J. Differential Geom., 2 (1968), 197-202, 369-384, 3 (1969), 83-94, 433-446.
WU2) H. Wu, On a problem concerning the intrinsic characterization of Cⁿ, Math. Ann., 246 (1979), 15-22.

Right : [FI] G. Fischer, Complex analytic geometry, Lecture Notes in Math., 538, Springer, Berlin-Heidelberg-New York, 1976.
[GR] H. Grauert, Bemerkenswerte pseudokonvexe Mannigfaltigkeiten, Math. Z., 81 (1963), 377-391.
[GUR] R. C. Gunning and H. Rossi, Analytic functions of several complex variables, Prentice-Hall, 1965.
[GW1] R. E. Greene and H. Wu, Integrals of subharmonic functions on manifolds of nonnegative curvature, Invent. Math., 27 (1974), 265-298.
[GW2] R. E. Greene and H. Wu, Function theory on manifolds which possesses a pole, Lecture Notes in Math., 699, Springer, Berlin-Heidelberg-New York, 1979.
[KA1] H. Kaneko, A stochastic approach to a Liouville property for plurisubharmonic functions, J. Math. Soc. Japan, 41 (1989), 291-299.
[KA2] H. Kaneko, Private communication.
[NO] J. Noguchi and T. Ochiai, Geometric function theory in several complex variables, Transl. Math. Monographs, 80, Amer. Math. Soc., 1990.
[RI] R. Richberg, Stetige streng pseudokonvexe Funktionen, Math. Ann., 175 (1968), 257-286.
[SIW] N. Sibony and P. M. Wong, Some remarks on the Casorati-Weierstrass' theorem, Ann. Polon. Math., 39 (1981), 165-174.
[ST1] W. Stoll, The growth of area of a transcendental analytic set I, II, Math. Ann., 156 (1964), 47-78, 144-170.
[ST2] W. Stoll, The Ahlfors-Weyl theory of meromorphic maps on parabolic manifolds, Lecture Notes in Math., 981, Springer, Berlin-Heidelberg-New York-Tokyo, 1983, pp. 101-219.
[TA1] K. Takegoshi, A non-existence theorem for pluriharmonic maps of finite energy, Math. Z., 192 (1986), 21-27.
[TA2] K. Takegoshi, Energy estimates and Liouville theorems for harmonic maps, Ann. Sci. École Norm. Sup., 23 (1990), 563-592.
[TU] Ch. Tung, The first main theorem of value distribution on complex spaces, Atti Acad. Naz. Lincei Mem. Cl. Sci. Fis. Mat. Natur. Sez. Ia (8), 15 (1979), 91-263.
[WU1] H. Wu, Remarks on the first main theorem in equidistribution theory, I, II, III, IV, J. Differential Geom., 2 (1968), 197-202, 369-384, 3 (1969), 83-94, 433-446.
[WU2] H. Wu, On a problem concerning the intrinsic characterization of Cⁿ, Math. Ann., 246 (1979), 15-22.

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