03428nam 22005535 450 99641825890331620200706050608.03-030-32068-510.1007/978-3-030-32068-3(CKB)4100000010953739(DE-He213)978-3-030-32068-3(MiAaPQ)EBC6173999(PPN)243761317(EXLCZ)99410000001095373920200411d2020 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierConformally Invariant Metrics and Quasiconformal Mappings[electronic resource] /by Parisa Hariri, Riku Klén, Matti Vuorinen1st ed. 2020.Cham :Springer International Publishing :Imprint: Springer,2020.1 online resource (XIX, 502 p. 56 illus.) Springer Monographs in Mathematics,1439-73823-030-32067-7 Includes bibliographical references and index.Part 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.This 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.Springer Monographs in Mathematics,1439-7382Potential theory (Mathematics)Differential geometryPotential Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M12163Differential Geometryhttps://scigraph.springernature.com/ontologies/product-market-codes/M21022Potential theory (Mathematics).Differential geometry.Potential Theory.Differential Geometry.515.9Hariri Parisaauthttp://id.loc.gov/vocabulary/relators/aut1005288Klén Rikuauthttp://id.loc.gov/vocabulary/relators/autVuorinen Mattiauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK996418258903316Conformally Invariant Metrics and Quasiconformal Mappings2311009UNISA