LEADER 03428nam 22005535 450 001 996418258903316 005 20200706050608.0 010 $a3-030-32068-5 024 7 $a10.1007/978-3-030-32068-3 035 $a(CKB)4100000010953739 035 $a(DE-He213)978-3-030-32068-3 035 $a(MiAaPQ)EBC6173999 035 $a(PPN)243761317 035 $a(EXLCZ)994100000010953739 100 $a20200411d2020 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aConformally Invariant Metrics and Quasiconformal Mappings$b[electronic resource] /$fby Parisa Hariri, Riku Klén, Matti Vuorinen 205 $a1st ed. 2020. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2020. 215 $a1 online resource (XIX, 502 p. 56 illus.) 225 1 $aSpringer Monographs in Mathematics,$x1439-7382 311 $a3-030-32067-7 320 $aIncludes bibliographical references and index. 327 $aPart I: Introduction and Review -- Introduction -- A Survey of QuasiregularMappings -- Part II: Conformal Geometry -- Möbius Transformations -- Hyperbolic Geometry -- Generalized Hyperbolic Geometries -- Metrics and Geometry -- Part III: Modulus and Capacity -- The Modulus of a Curve Family -- The Modulus as a Set Function -- The Capacity of a Condenser -- Conformal Invariants -- Part IV: Intrinsic Geometry -- Hyperbolic Type Metrics -- Comparison of Metrics -- Local Convexity of Balls -- Inclusion Results for Balls -- Part V: QuasiregularMappings -- Basic Properties of QuasiregularMappings -- Distortion Theory -- Dimension-Free Theory -- Metrics and Maps -- Teichmüller?s Displacement Problem -- Part VI: Solutions -- Solutions to Exercises. 330 $aThis book is an introduction to the theory of quasiconformal and quasiregular mappings in the euclidean n-dimensional space, (where n is greater than 2). There are many ways to develop this theory as the literature shows. The authors' approach is based on the use of metrics, in particular conformally invariant metrics, which will have a key role throughout the whole book. The intended readership consists of mathematicians from beginning graduate students to researchers. The prerequisite requirements are modest: only some familiarity with basic ideas of real and complex analysis is expected. 410 0$aSpringer Monographs in Mathematics,$x1439-7382 606 $aPotential theory (Mathematics) 606 $aDifferential geometry 606 $aPotential Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M12163 606 $aDifferential Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21022 615 0$aPotential theory (Mathematics). 615 0$aDifferential geometry. 615 14$aPotential Theory. 615 24$aDifferential Geometry. 676 $a515.9 700 $aHariri$b Parisa$4aut$4http://id.loc.gov/vocabulary/relators/aut$01005288 702 $aKlén$b Riku$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aVuorinen$b Matti$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996418258903316 996 $aConformally Invariant Metrics and Quasiconformal Mappings$92311009 997 $aUNISA