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Erschienen in:
Function Spaces of Polyanalytic Functions Kapitel lesen Erstes Kapitel lesen

2014 | OriginalPaper | Buchkapitel

The Schwarz Lemma: Rigidity and Dynamics

verfasst von : Mark Elin, Fiana Jacobzon, Marina Levenshtein, David Shoikhet

Erschienen in: Harmonic and Complex Analysis and its Applications

Verlag: Springer International Publishing

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Abstract

The Schwarz Lemma has given impetus to developments in several areas of complex analysis and mathematics in general. We survey some investigations related to its three parts (invariance, rigidity, and distortion) that began early in the twentieth century and are still being carried out. We consider only functions analytic in the unit disk. Special attention is devoted to the Boundary Schwarz Lemma and to applications of the Schwarz–Pick Lemma and the Boundary Schwarz Lemma to modern rigidity theory and complex dynamics.

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Vorheriges Kapitel Classical and Stochastic Löwner–Kufarev Equations
Nächstes Kapitel Coorbit Theory and Bergman Spaces
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Metadaten
Titel
The Schwarz Lemma: Rigidity and Dynamics
verfasst von
Mark Elin
Fiana Jacobzon
Marina Levenshtein
David Shoikhet
Copyright-Jahr
2014
Buch
Harmonic and Complex Analysis and its Applications

Print ISBN: 978-3-319-01805-8

Electronic ISBN: 978-3-319-01806-5

Copyright-Jahr: 2014

DOI
https://doi.org/10.1007/978-3-319-01806-5_3