LEADER 04050nam 22006015 450 001 9910480079303321 005 20200703063651.0 010 $a3-662-02770-4 024 7 $a10.1007/978-3-662-02770-7 035 $a(CKB)2660000000026958 035 $a(SSID)ssj0001296022 035 $a(PQKBManifestationID)11754018 035 $a(PQKBTitleCode)TC0001296022 035 $a(PQKBWorkID)11343721 035 $a(PQKB)10534616 035 $a(DE-He213)978-3-662-02770-7 035 $a(MiAaPQ)EBC3097408 035 $a(PPN)238024636 035 $a(EXLCZ)992660000000026958 100 $a20130107d1992 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aBoundary Behaviour of Conformal Maps$b[electronic resource] /$fby Christian Pommerenke 205 $a1st ed. 1992. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d1992. 215 $a1 online resource (IX, 300 p.) 225 1 $aGrundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics,$x0072-7830 ;$v299 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-54751-7 311 $a3-642-08129-0 320 $aIncludes bibliographical references and index. 327 $a1. 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. 330 $aWe study the boundary behaviour of a conformal map of the unit disk onto an arbitrary simply connected plane domain. A principal aim of the theory is to obtain a one-to-one correspondence between analytic properties of the function and geometrie properties of the domain. In the classical applications of conformal mapping, the domain is bounded by a piecewise smooth curve. In many recent applications however, the domain has a very bad boundary. It may have nowhere a tangent as is the case for Julia sets. Then the conformal map has many unexpected properties, for instance almost all the boundary is mapped onto almost nothing and vice versa. The book is meant for two groups of users. (1) Graduate students and others who, at various levels, want to learn about conformal mapping. Most sections contain exercises to test the understand­ ing. They tend to be fairly simple and only a few contain new material. Pre­ requisites are general real and complex analyis including the basic facts about conformal mapping (e.g. AhI66a). (2) Non-experts who want to get an idea of a particular aspect of confor­ mal mapping in order to find something useful for their work. Most chapters therefore begin with an overview that states some key results avoiding tech­ nicalities. The book is not meant as an exhaustive survey of conformal mapping. Several important aspects had to be omitted, e.g. numerical methods (see e.g. 410 0$aGrundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics,$x0072-7830 ;$v299 606 $aFunctions of complex variables 606 $aPhysical measurements 606 $aMeasurement    606 $aFunctions of a Complex Variable$3https://scigraph.springernature.com/ontologies/product-market-codes/M12074 606 $aMeasurement Science and Instrumentation$3https://scigraph.springernature.com/ontologies/product-market-codes/P31040 615 0$aFunctions of complex variables. 615 0$aPhysical measurements. 615 0$aMeasurement   . 615 14$aFunctions of a Complex Variable. 615 24$aMeasurement Science and Instrumentation. 676 $a515.9 700 $aPommerenke$b Christian$4aut$4http://id.loc.gov/vocabulary/relators/aut$058237 906 $aBOOK 912 $a9910480079303321 996 $aBoundary behaviour of conformal maps$9382721 997 $aUNINA