LEADER 03075nam 2200601 450 001 996466514803316 005 20220520144954.0 010 $a3-540-39207-6 024 7 $a10.1007/BFb0077904 035 $a(CKB)1000000000437486 035 $a(SSID)ssj0000322255 035 $a(PQKBManifestationID)12099099 035 $a(PQKBTitleCode)TC0000322255 035 $a(PQKBWorkID)10282834 035 $a(PQKB)10059196 035 $a(DE-He213)978-3-540-39207-1 035 $a(MiAaPQ)EBC5585483 035 $a(Au-PeEL)EBL5585483 035 $a(OCoLC)1066188412 035 $a(MiAaPQ)EBC6842918 035 $a(Au-PeEL)EBL6842918 035 $a(PPN)155176781 035 $a(EXLCZ)991000000000437486 100 $a20220303d1988 uy 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aConformal geometry and quasiregular mappings /$fMatti Vuorinen 205 $a1st ed. 1988. 210 1$aBerlin ;$aHeidelberg :$cSpringer-Verlag,$d[1988] 210 4$dİ1988 215 $a1 online resource (XXII, 214 p.) 225 1 $aLecture Notes in Mathematics ;$v1319 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a0-387-19342-1 311 $a3-540-19342-1 327 $aConformal geometry -- Modulus and capacity -- Quasiregular mappings -- Boundary behavior. 330 $aThis book is an introduction to the theory of spatial quasiregular mappings intended for the uninitiated reader. At the same time the book also addresses specialists in classical analysis and, in particular, geometric function theory. The text leads the reader to the frontier of current research and covers some most recent developments in the subject, previously scatterd through the literature. A major role in this monograph is played by certain conformal invariants which are solutions of extremal problems related to extremal lengths of curve families. These invariants are then applied to prove sharp distortion theorems for quasiregular mappings. One of these extremal problems of conformal geometry generalizes a classical two-dimensional problem of O. Teichmüller. The novel feature of the exposition is the way in which conformal invariants are applied and the sharp results obtained should be of considerable interest even in the two-dimensional particular case. This book combines the features of a textbook and of a research monograph: it is the first introduction to the subject available in English, contains nearly a hundred exercises, a survey of the subject as well as an extensive bibliography and, finally, a list of open problems. 410 0$aLecture notes in mathematics (Springer-Verlag) ;$v1319. 606 $aComplex analysis 615 0$aComplex analysis. 676 $a613.283 686 $a30C60$2msc 700 $aVuorinen$b Matti$059551 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466514803316 996 $aConformal geometry and quasiregular mappings$978604 997 $aUNISA