LEADER 03963nam 22005775 450 001 9910765481103321 005 20240626161120.0 010 $a3-031-45418-9 024 7 $a10.1007/978-3-031-45418-9 035 $a(MiAaPQ)EBC30954332 035 $a(Au-PeEL)EBL30954332 035 $a(DE-He213)978-3-031-45418-9 035 $a(CKB)28887498100041 035 $a(EXLCZ)9928887498100041 100 $a20231118d2023 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aMappings with Direct and Inverse Poletsky Inequalities /$fby Evgeny Sevost'yanov 205 $a1st ed. 2023. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2023. 215 $a1 online resource (437 pages) 225 1 $aDevelopments in Mathematics,$x2197-795X ;$v78 311 08$aPrint version: Sevost'yanov, Evgeny Mappings with Direct and Inverse Poletsky Inequalities Cham : Springer,c2023 9783031454172 327 $aGeneral definitions and notation -- Boundary behavior of mappings with Poletsky inequality -- Removability of singularities of generalized quasiisometries -- Normal families of generalized quasiisometries -- On boundary behavior of mappings with Poletsky inequality in terms of prime ends -- Local and boundary behavior of mappings on Riemannian manifolds -- Local and boundary behavior of maps in metric spaces -- On Sokhotski-Casorati-Weierstrass theorem on metric spaces -- On boundary extension of mappings in metric spaces in the terms of prime ends -- On the openness and discreteness of mappings with the inverse Poletsky inequality -- Equicontinuity and isolated singularities of mappings with the inverse Poletsky inequality -- Equicontinuity of families of mappings with the inverse Poletsky inequality in terms of prime ends -- Logarithmic H¨older continuous mappings and Beltrami equation -- On logarithmic H¨older continuity of mappings on the boundary -- The Poletsky and V¨ais¨al¨a inequalities for the mappings with (p;q)-distortion -- An analog of the V¨ais¨al¨a inequality for surfaces -- Modular inequalities on Riemannian surfaces -- On the local and boundary behavior of mappings of factor spaces -- References -- Index. 330 $aThe monograph is devoted to the use of the moduli method in mapping theory, in particular, the meaning of direct and inverse modulus inequalities and their possible applications. The main goal is the development of a modulus technique in the Euclidean space and some metric spaces (manifolds, surfaces, quotient spaces, etc.). Particular attention is paid to the local and boundary behavior of mappings, as well as to obtaining modulus inequalities for some classes. The reader is invited to familiarize himself with all the main achievements of the author, synthesized in this book. The results presented here are of a high scientific level, are new and have no analogues in the world with such a degree of generality. 410 0$aDevelopments in Mathematics,$x2197-795X ;$v78 606 $aFunctions of complex variables 606 $aPotential theory (Mathematics) 606 $aFunctions of a Complex Variable 606 $aPotential Theory 606 $aFuncions de variables complexes$2thub 606 $aTeoria del potencial (Matemātica)$2thub 608 $aLlibres electrōnics$2thub 615 0$aFunctions of complex variables. 615 0$aPotential theory (Mathematics). 615 14$aFunctions of a Complex Variable. 615 24$aPotential Theory. 615 7$aFuncions de variables complexes 615 7$aTeoria del potencial (Matemātica) 676 $a515.9 700 $aSevost'yanov$b Evgeny$01448840 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910765481103321 996 $aMappings with Direct and Inverse Poletsky Inequalities$93644676 997 $aUNINA