دانلود کتاب Invariant Distances and Metrics in Complex Analysis

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Preface\nI Hyperbolic geometry of the unit disc\nExercises\nII The Carathéodory pseudodistance and the Carathéodory-Reiffen pseudometric\n2.1 Definitions. General Schwarz-Pick Lemma\n2.2 Balanced domains\n2.3 Carathéodory hyperbolicity\n2.4 The Carathéodory topology\n2.5 Properties of c(*)and γ. Length of curve. Inner Carathéodory pseudodistance\n2.6 Two applications\n2.7 A class of n-circled domains\nNotes\nExercises\nIII The Kobayashi pseudodistance and the Kobayashi-Royden pseudometric\n3.1 The Lempert function and the Kobayashi pseudodistance\n3.2 Tautness\n3.3 General properties of k\n3.4 An extension theorem\n3.5 The Kobayashi-Royden pseudometric\n3.6 The Kobayashi-Buseman pseudometric\n3.7 Product-formula\nNotes\nExercises\nIV Contractible systems\n4.1 Abstract point of view\n4.2 Extremal problems for plurisubharmonic functions\n4.3 Inner pseudodistances. Integrated forms. Derivatives. Buseman pseudometrics. C1-pseudodistances\n4.4 Example – elementary n-circled domains\nNotes\nExercises\nV Contractible functions and metrics for the annulus\nNotes\nExercises\nVI The Bergman metric\n6.1 The Bergman kernel\n6.2 The Bergman pseudometric\n6.3 Comparison and localization\n6.4 The Skwarczyński pseudometric\nNotes\nExercises\nVII Hyperbolicity and completeness\n7.1 Global hyperbolicity\n7.2 Local hyperbolicity\n7.3 Completeness – general discussion\n7.4 Carathéodory completeness\n7.5 Kobayashi completeness\n7.6 Bergman completeness\nNotes\nExercises\nVIII Complex geodesics. Lempert’s theorem\n8.1 Complex geodesics\n8.2 Lempert’s theorem\n8.3 Uniqueness of complex geodesies\n8.4 Geodesics in convex complex ellipsoids\n8.5 Biholomorphisms of complex ellipsoids\n8.6 Schwarz Lemma – the case of equality\n8.7 Criteria for biholomorphicity\nNotes\nExercises\nIX Product-property\nExercises\nX Comparison on strongly pseudoconvex domains\n10.1 Strongly pseudoconvex domains\n10.2 The boundary behavior of the Carathéodory and the Kobayashi distances\n10.3 Localization\n10.4 Boundary behavior of the Carathéodory-Reiffen and the Kobayashi-Royden metrics\n10.5 A comparison of distances\n10.6 Characterization of the unit ball by its automorphism group\nNotes\nExercises\nMiscellanea\nA The automorphism group of bounded domains\nB Holomorphic curvature\nC Complex geodesics\nD Criteria for biholomorphicity\nE Boundary behavior of contractible metrics on weakly pseudoconvex domains\nAppendix\nHF Holomorphic functions\nPSH Subharmonic and plurisubharmonic functions\nPSC Domains of holomorphy and pseudoconvex domains\nAUT Automorphisms\nAutomorphisms of the unit disc\nAutomorphisms of the unit polydisc\nAutomorphisms of the unit Euclidean ball\nGR Green function and Dirichlet problem\nMA Monge-Ampère operator\nH Hardy spaces\nReferences\nList of symbols\nIndex