ON THE GEOMETRY OF MEROMORPHIC FUNCTIONS
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This paper establishes various propositions characterizing the geometric behavior of meromorphic functions in . Distortion theorems for these functions form a basis for the arguments. Namely, a finite number of nice curves , , in the -plane are considered (in particular, may be a straight line) and information is obtained about the lengths of the sets , . Qualitatively, the main result is as follows: on some sequence where is an absolute constant, and is the Ahlfors characteristic.Bibliography: 29 titles.
length- area principle, Riemann surface, branching, meromorphic functions, distortion, Meromorphic functions of one complex variable (general theory), Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
length- area principle, Riemann surface, branching, meromorphic functions, distortion, Meromorphic functions of one complex variable (general theory), Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
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