Titlebook: Continuous Semigroups of Holomorphic Self-maps of the Unit Disc; Filippo Bracci,Manuel D. Contreras,Santiago Díaz-M Book 2020 Springer Nat

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Menschliches Verkaufen: Erfolg ist machbarIn this chapter we introduce the last two tools we need in our study of semigroups throughout the book. The first one comes from potential theory: the harmonic measure of a simply connected domain in . related to a subset of its boundary. The second one is the notion of Bloch function and related maximum principles and distortion theorems.

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Carathéodory’s Prime Ends TheoryThe aim of this chapter is to introduce prime ends and the Carathéodory topology of simply connected domains and see how impressions of prime ends are related to unrestricted limits and principal parts of prime ends can be used to understand the non-tangential behavior of univalent functions. Finally, we prove Carathéodory’s extension theorems.

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Hyperbolic Geometry and Iteration Theoryy of the unit disc, the complex plane and the Riemann sphere. Next, from Schwarz’s Lemma, we define the hyperbolic metric and hyperbolic distance of the unit disc, and extend, . Kobayashi, the concept of hyperbolic distance to Riemann surfaces. We turn then our attention to the analytical and dynami

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