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CURVES, DOMAINS AND PICARD'S THEOREM

Published online by Cambridge University Press:  15 March 2002

GUANG YUAN ZHANG
GUANG YUAN ZHANG
Affiliation:
Department of Mathematical Sciences, Tsinghua University, Beijing 100084, The People's Republic of [email protected]
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Abstract

Based on computing spherical lengths of polygonal curves and spherical areas of domains bounded by polygonal curves on the complex plane, this paper proves a property of holomorphic functions and, as an application, gives a very brief proof of a famous inequality obtained by L. V. Ahlfors which easily implies Picard's theorem. Taken together with the arguments given by Alhfors, therefore, this paper in fact gives an elementary, brief and geometrical proof of Picard's theorem.

Type
PAPERS
Information
Bulletin of the London Mathematical Society , Volume 34 , Issue 2 , March 2002 , pp. 205 - 211
Copyright
© 2002 The London Mathematical Society

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