科研之友
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摘要
Let f be a holomorphic function of the unit disc D, preserving the origin. According to Schwarz's Lemma, vertical bar f' (0)vertical bar <= 1, provided that f (D) subset of D. We prove that this bound still holds, assuming only that f (D) does not contain any closed rectilinear segment [0, e(i phi)], phi epsilon [0, 2 pi], i.e., does not contain any entire radius of the closed unit disc. Furthermore, we apply this result to the hyperbolic density and give a covering theorem.
- 出版日期2016-3
