LEADER 04528nam 22007935 450 001 9910983330603321 005 20250905125141.0 010 $a9783031772047 010 $a3031772040 024 7 $a10.1007/978-3-031-77204-7 035 $a(CKB)37391393400041 035 $a(MiAaPQ)EBC31892428 035 $a(Au-PeEL)EBL31892428 035 $a(DE-He213)978-3-031-77204-7 035 $a(OCoLC)1499722222 035 $a(EXLCZ)9937391393400041 100 $a20250129d2025 u| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 14$aThe Geometric Theory of Complex Variables /$fby Peter V. Dovbush, Steven G. Krantz 205 $a1st ed. 2025. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2025. 215 $a1 online resource (1074 pages) 311 08$a9783031772030 311 08$a3031772032 327 $a- Introduction -- The Riemann Mapping Theorem -- The Ahlfors Map -- A Riemann Mapping Theorem for Two-Connected Domains in the Plane -- Riemann Multiply Connected Domains -- Quasiconformal Mappings -- Manifolds -- Riemann Surfaces -- The Uniformization Theorem -- Automorphism Groups -- Ridigity of Holomorphic Mappings and a New Schwarz Lemma at the Boundary -- The Schwarz Lemma and Its Generalizations -- Invariant Distances on Complex Manifolds -- Hyperbolic Manifolds -- The Fatou Theory and Related Matters -- The Theorem of Bun Wong and Rosay -- Smoothness to the Boundary of Biholomorphic Mappings -- Solution ? problem -- Harmonic measure -- Quadrature -- Teichmüller Theory -- Bibliography -- Index. 330 $aThis book provides the reader with a broad introduction to the geometric methodology in complex analysis. It covers both single and several complex variables, creating a dialogue between the two viewpoints. Regarded as one of the 'grand old ladies' of modern mathematics, complex analysis traces its roots back 500 years. The subject began to flourish with Carl Friedrich Gauss's thesis around 1800. The geometric aspects of the theory can be traced back to the Riemann mapping theorem around 1850, with a significant milestone achieved in 1938 with Lars Ahlfors's geometrization of complex analysis. These ideas inspired many other mathematicians to adopt this perspective, leading to the proliferation of geometric theory of complex variables in various directions, including Riemann surfaces, Teichmüller theory, complex manifolds, extremal problems, and many others. This book explores all these areas, with classical geometric function theory as its main focus. Its accessible and gentle approach makes it suitable for advanced undergraduate and graduate students seeking to understand the connections among topics usually scattered across numerous textbooks, as well as experienced mathematicians with an interest in this rich field. 606 $aGlobal analysis (Mathematics) 606 $aManifolds (Mathematics) 606 $aFunctions of complex variables 606 $aFunctional analysis 606 $aGlobal Analysis and Analysis on Manifolds 606 $aSeveral Complex Variables and Analytic Spaces 606 $aFunctional Analysis 606 $aAnàlisi global (Matemàtica)$2thub 606 $aVarietats complexes$2thub 606 $aFuncions de variables complexes$2thub 606 $aAnàlisi funcional$2thub 606 $aAnàlisi global (Matemàtica)$2thub 606 $aAnàlisi de variància$2thub 606 $aEspais analítics$2thub 608 $aLlibres electrònics$2thub 615 0$aGlobal analysis (Mathematics) 615 0$aManifolds (Mathematics) 615 0$aFunctions of complex variables. 615 0$aFunctional analysis. 615 14$aGlobal Analysis and Analysis on Manifolds. 615 24$aSeveral Complex Variables and Analytic Spaces. 615 24$aFunctional Analysis. 615 7$aAnàlisi global (Matemàtica) 615 7$aVarietats complexes 615 7$aFuncions de variables complexes 615 7$aAnàlisi funcional 615 7$aAnàlisi global (Matemàtica) 615 7$aAnàlisi de variància 615 7$aEspais analítics 676 $a514.74 700 $aDovbush$b Peter V$01786169 701 $aKrantz$b Steven G$055961 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910983330603321 996 $aThe Geometric Theory of Complex Variables$94317564 997 $aUNINA