Abstract
We establish an estimate for the degree of a holomorphic mapping f : K 1 → K 2 (here, K 1 and K 2 are doubly-connected domains) in terms of the modulus of a family of curves in K 2. This estimate generalizes a result obtained by Kobayashi.
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REFERENCES
S. Kobayashi, Hyperbolic Manifolds and Holomorphic Mappings, Marcel Dekker, New York (1970).
L. V. Ahlfors, Conformal Invariants—Topics in Geometric Functional Theory, McGraw-Hill, New York (1973).
M. A. Chinac, “Isoperimetric property of modulus and quasiconformal maps,” Sib. Mat. Zh., 27, 152–160 (1986).
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, No. 8, pp. 1135–1138, August, 2004.
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Tuan, N.D., Duc, P.V. On the degree of holomorphic mappings from an annulus into an annulus. Ukr Math J 56, 1353–1357 (2004). https://doi.org/10.1007/s11253-005-0062-5
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DOI: https://doi.org/10.1007/s11253-005-0062-5