Complex Analysis and Geometry [[electronic resource] ] : KSCV10, Gyeongju, Korea, August 2014 / / edited by Filippo Bracci, Jisoo Byun, Hervé Gaussier, Kengo Hirachi, Kang-Tae Kim, Nikolay Shcherbina

• Pubblicazione: Tokyo : , : Springer Japan : , : Imprint : Springer, , 2015
• Edizione: 1st ed. 2015.
• Descrizione fisica: 1 online resource (370 p.)
• Disciplina: 516.362
• Soggetto topico: Functions of complex variables; Algebraic geometry; Differential geometry; Several Complex Variables and Analytic Spaces; Algebraic Geometry; Functions of a Complex Variable; Differential Geometry
• Persona (resp. second.): BracciFilippo; ByunJisoo; GaussierHervé; HirachiKengo; KimKang-Tae; ShcherbinaNikolay
• Note generali: "KSCV10 (the 10th) Symposium was held during 7-11 July 2014, as a satellite conference to the ICM"--Preface.
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: Preface; Contents; Fatou Flowers and Parabolic Curves; 1 The Original Leau-Fatou Flower Theorem; 2 Écalle-Hakim Theory; 3 Blow-Ups, Indices and Fatou Flowers; 4 Parabolic Domains; 5 The Formal Infinitesimal Generator ; 6 Homogeneous Vector Fields and Geodesics; 7 Other Systems with Parabolic Behavior; References; A CR Proof for a Global Estimate of the Diederich--Fornaess Index of Levi-Flat Real Hypersurfaces; 1 Introduction; 2 Preliminaries; 2.1 Levi-Flat CR Manifold; 2.2 Description on Foliated Charts; 2.3 The Diederich--Fornaess Index; 3 The Proof of Lemma 1 and a Remark ; 3.1 Proof of Lemma 13.2 The Approach of Bejancu and Deshmukh; 3.3 Open Question; References; Unbounded Pseudoconvex Domains in mathbbCn and Their Invariant Metrics; 1 Some Problems; 2 A Remark on Hahn-Lu Comparison Theorem; 3 A Technique for Positivity and Completeness of Bergman Metric; 4 Examples; 4.1 The Kohn-Nirenberg and Fornaess Domains; 4.2 Other Domains; 5 Remarks and More Questions; References; Abstract Basins of Attraction; 1 The Construction of Abstract Basins; 2 Bedford's Conjecture; 3 Loewner's Theory; 4 Models; References; Invertible Dynamics on Blow-ups of mathbbPk ; 1 Introduction2 Rational Surfaces; 3 Degree Complexity, or Dynamical Degree; 4 Some Rational Surface Automorphisms with δ>1; 5 Connection Between Dynamical Degree and Length Growth: A Graphic Example ; 6 Heuristic Picture: Dynamical Complexity Versus Degree Complexity ; 7 What Are the Compact Surfaces X Which Carry an finAut(X) with δ1(f)>1?; 8 Pseudo-automorphisms; 9 Intermediate Dynamical Degrees; 10 Existence of Pseudo-automorphisms of Blowups of mathbbPk ; 11 Cohomological Hyperbolicity; References ; On Nazarov's Complex Analytic Approach to the Mahler Conjecture and the Bourgain-Milman Inequality1 Introduction; 2 Equivalent SCV Formulation; 3 The Upper Bound; 4 The Lower Bound; References; A Survey on Bergman Completeness; 1 Introduction; 2 Bergman Completeness for Domains in mathbbCn; 3 Bergman Completeness for Open Complex Manifolds; References; Structure Theorems for Compact Kähler Manifolds with Nef Anticanonical Bundles; 1 Introduction and Preliminaries; 2 Criterion for Rational Connectedness; 3 A Generalized Holonomy Principle ; 4 Structure Theorem for Compact Kähler Manifolds with KX-1 Semipositive5 Compact Kähler Manifolds with Nef Anticanonical Bundles; References; An Estimate for the Squeezing Function and Estimates of Invariant Metrics; 1 Introduction; 2 Proof of Theorem 1.2; 3 Proof of Theorem 1.1; 3.1 Estimate (a); 3.2 Estimate (b); 4 An Example; References; Classification of Proper Holomorphic Mappings Between Generalized Pseudoellipsoids of Different Dimensions; 1 The Research of Proper Holomorphic Mappings; 1.1 Extension Problem; 1.2 Proper Holomorphic Mappings and Biholomorphic Mappings ; 1.3 Determination of Proper Holomorphic Mappings
• Sommario/riassunto: This volume includes 28 chapters by authors who are leading researchers of the world describing many of the up-to-date aspects in the field of several complex variables (SCV). These contributions are based upon their presentations at the 10th Korean Conference on Several Complex Variables (KSCV10), held as a satellite conference to the International Congress of Mathematicians (ICM) 2014 in Seoul, Korea. SCV has been the term for multidimensional complex analysis, one of the central research areas in mathematics. Studies over time have revealed a variety of rich, intriguing, new knowledge in complex analysis and geometry of analytic spaces and holomorphic functions which were "hidden" in the case of complex dimension one. These new theories have significant intersections with algebraic geometry, differential geometry, partial differential equations, dynamics, functional analysis and operator theory, and sheaves and cohomology, as well as the traditional analysis of holomorphic functions in all dimensions. This book is suitable for a broad audience of mathematicians at and above the beginning graduate-student level. Many chapters pose open-ended problems for further research, and one in particular is devoted to problems for future investigations.
• Titolo autorizzato: Complex analysis and geometry
• ISBN: 4-431-55744-X
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910299776203321
• Lo trovi qui: Univ. Federico II
• Serie: Springer Proceedings in Mathematics & Statistics, . 2194-1009 ; ; 144