Lemniscate Zone and Distortion Theorems for Multivalent Functions. II
For meromorphic circumferentially mean p-valent functions, an analog of the classical distortion theorem is proved. It is shown that the existence of connected lemniscates of the function and a constraint on a cover of two given points lead to an inequality involving the Green energy of a discrete signedmeasure concentrated at the zeros of the given function and the absolute values of its derivatives at these zeros. This inequality is an equality for the superposition of a certain univalent function and an appropriate Zolotarev fraction.
Keywordsmeromorphic function p-valent function lemniscate Zolotarev fraction symmetrization
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