Nevanlinna Theory by Kunihiko Kodaira

Author:Kunihiko Kodaira
Language: eng
Format: epub, pdf
Publisher: Springer Singapore, Singapore

Namely, , whence follows. Since , c is at most 1. We shall show that holds for any holomorphic map We may assume that , so that it suffices to prove that the modulus of the Jacobian

does not exceed 1.

Let

be the Taylor series.

By assumption,

if and . By the Schwarz Lemma (3.1),

Hence if , so that one has .

Therefore

Given , let be the set of such that are holomorphic maps and are subsets of such that .

Since

by taking the lower limit one has

Therefore with , so that since one has already .

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