On the behavior of meromorphic functions around some nonisolated singularities. II.
Järvi, Pentti (1995)
Annales Academiae Scientiarum Fennicae. Series A I. Mathematica
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Järvi, Pentti (1995)
Annales Academiae Scientiarum Fennicae. Series A I. Mathematica
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Gerd-E. Dethloff (1989)
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Arkadiusz Lewandowski (2012)
Annales Polonici Mathematici
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The main result of the paper is a new Hartogs type extension theorem for generalized (N,k)-crosses with analytic singularities for separately holomorphic functions and for separately meromorphic functions. Our result is a simultaneous generalization of several known results, from the classical cross theorem, through the extension theorem with analytic singularities for generalized crosses, to the cross theorem with analytic singularities for meromorphic functions.
Walter Bergweiler, Alexander Eremenko (1995)
Revista Matemática Iberoamericana
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Our main result implies the following theorem: Let f be a transcendental meromorphic function in the complex plane. If f has finite order ρ, then every asymptotic value of f, except at most 2ρ of them, is a limit point of critical values of f. We give several applications of this theorem. For example we prove that if f is a transcendental meromorphic function then f'fn with n ≥ 1 takes every finite non-zero value infinitely often. This proves a conjecture...
Olli Lehto (1959)
Commentarii mathematici Helvetici
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Jörg Winkler, Sakari Toppila (1982)
Mathematische Zeitschrift
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H. S. Gopalakrishna, Subhas S. Bhoosnurmath (1977)
Annales Polonici Mathematici
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H. S. Gopalakrishna, Subhas S. Bhoosnurmath (1976)
Annales Polonici Mathematici
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Buchner, Klaus (1997)
General Mathematics
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Evgeny M. Chirka (1996)
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If E is a closed subset of locally finite Hausdorff (2n-2)-measure on an n-dimensional complex manifold Ω and all the points of E are nonremovable for a meromorphic mapping of Ω E into a compact Kähler manifold, then E is a pure (n-1)-dimensional complex analytic subset of Ω.
Yuxian Chen, Zhaojun Wu (2012)
Annales Polonici Mathematici
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This paper is devoted to exceptional values of meromorphic functions and of their derivatives on annuli. Some facts on exceptional values for meromorphic functions in the complex plane which were established by Singh, Gopalakrishna and Bhoosnurmath [Math. Ann. 191 (1971), 121-142, and Ann. Polon. Math. 35 (1977/78), 99-105] will be considered on annuli.
S. K. Singh, V. N. Kulkarni (1973)
Annales Polonici Mathematici
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G.J. Martin, D.B. Gauld (1993)
Mathematica Scandinavica
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S. K. Bajpai, T. J. S. Mehrok (1975)
Annales Polonici Mathematici
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