Complex Analysis and Geometry: KSCV10, Gyeongju, Korea, August 2014 (Springer Proceedings in Mathematics & Statistics Book 144)

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. Front Matter....Pages i-ix Fatou Flowers and Parabolic Curves....Pages 1-39 A CR Proof for a Global Estimate of the Diederich–Fornaess Index of Levi-Flat Real Hypersurfaces....Pages 41-48 Abstract Basins of Attraction....Pages 49-55 On Nazarov’s Complex Analytic Approach to the Mahler Conjecture and the Bourgain-Milman Inequality....Pages 57-66 A Survey on Bergman Completeness....Pages 67-88 Structure Theorems for Compact Kähler Manifolds with Nef Anticanonical Bundles....Pages 89-98 An Estimate for the Squeezing Function and Estimates of Invariant Metrics....Pages 99-117 Classification of Proper Holomorphic Mappings Between Generalized Pseudoellipsoids of Different Dimensions....Pages 119-133 Bergman Kernel Asymptotics and a Pure Analytic Proof of the Kodaira Embedding Theorem....Pages 135-147 On the Density and the Volume Density Property....Pages 149-159 On Meromorphic Continuation of Local Zeta Functions....Pages 161-173 Themes on Non-analytic Singularities of Plurisubharmonic Functions....Pages 175-186 Proper Holomorphic Maps Between Bounded Symmetric Domains....Pages 187-195 Characterizations of Strongly Pseudoconvex Models in Almost Complex and CR Geometries....Pages 197-206 Compact Smooth but Non-complex Complements of Complete Kähler Manifolds....Pages 207-219 Injectivity Theorems with Multiplier Ideal Sheaves and Their Applications....Pages 221-233 Amoebas of Cuspidal Strata for Classical Discriminant....Pages 235-239 A Remark on Hörmander’s Isomorphism....Pages 241-255 The Julia-Wolff-Carathéodory Theorem and Its Generalizations....Pages 257-272 A Brief Survey on Local Holomorphic Dynamics in Higher Dimensions....Pages 273-280 Proper Holomorphic Maps Between Bounded Symmetric Domains....Pages 281-293 Some Dynamical Systems of Extremal Measures....Pages 295-307 On Representative Domains and Cartan’s Theorem....Pages 309-318 On Curvature Estimates of Bounded Domains....Pages 319-326 Some Problems....Pages 327-342 ....Pages 343-351