Digons and Angular Derivatives of Analytic Self-maps of the Unit Disk
نویسنده
چکیده
We present a geometric approach to a well-known sharp inequality, due to Cowen and Pommerenke, about angular derivatives of general univalent self-maps of the unit disk.
منابع مشابه
Lower Schwarz–pick Estimates and Angular Deirivatives
The well-known Schwarz–Pick lemma states that any analytic mapping φ of the unit disk U into itself satisfies the inequality |φ′(z)| ≤ 1− |φ(z)| 2 1− |z|2 , z ∈ U. This estimate remains the same if we restrict ourselves to univalent mappings. The lower estimate is |φ′(z)| ≥ 0 generally or |φ′(z)| > 0 for univalent functions. To make the lower estimate nontrivial we consider univalent functions ...
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