Boundary Behaviour of Conformal Maps [[electronic resource] /] / by Christian Pommerenke

• Record Nr.: UNINA9910792492903321
• Autore: Pommerenke Christian
• Pubbl/distr/stampa: Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 1992
• ISBN: 3-662-02770-4
• Edizione: [1st ed. 1992.]
• Descrizione fisica: 1 online resource (IX, 300 p.)
• Collana: Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, , 0072-7830 ; ; 299
• Disciplina: 515.9
• Soggetti: Functions of complex variables; Physical measurements; Measurement ; Functions of a Complex Variable; Measurement Science and Instrumentation
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Bibliographic Level Mode of Issuance: Monograph
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: 1. Some Basic Facts -- 2. Continuity and Prime Ends -- 3. Smoothness and Corners -- 4. Distortion -- 5. Quasidisks -- 6. Linear Measure -- 7. Smirnov and Lavrentiev Domains -- 8. Integral Means -- 9. Curve Families and Capacity -- 10. Hausdorff Measure -- 11. Local Boundary Behaviour -- References -- Author Index.
• Sommario/riassunto: We study the boundary behaviour of a conformal map of the unit disk onto an arbitrary simply connected plane domain. A principal aim of the theory is to obtain a one-to-one correspondence between analytic properties of the function and geometrie properties of the domain. In the classical applications of conformal mapping, the domain is bounded by a piecewise smooth curve. In many recent applications however, the domain has a very bad boundary. It may have nowhere a tangent as is the case for Julia sets. Then the conformal map has many unexpected properties, for instance almost all the boundary is mapped onto almost nothing and vice versa. The book is meant for two groups of users. (1) Graduate students and others who, at various levels, want to learn about conformal mapping. Most sections contain exercises to test the understand­ ing. They tend to be fairly simple and only a few ; contain new material. Pre­ requisites are general real and complex analysis including the basic facts about conformal mapping (e.g. AhI66a). (2) Non-experts who want to get an idea of a particular aspect of confor­ mal mapping in order to find something useful for their work. Most chapters therefore begin with an overview that states some key results avoiding tech­ nicalities. The book is not meant as an exhaustive survey of conformal mapping. Several important aspects had to be omitted, e.g. numerical methods (see e.g.