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Complex Analysis and Geometry

KSCV10, Gyeongju, Korea, August 2014

  • Conference proceedings
  • © 2015

Overview

Editors:
  1. Filippo Bracci

    1. Department of Mathematics, Università di Roma Tor Vergata, Rome, Italy

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  2. Jisoo Byun

    1. Dept. of Mathematics Education, Kyungnam University, Changwon, Korea (Republic of)

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  3. Hervé Gaussier

    1. Université Joseph Fourier Grenoble, Institut Fourier, Grenoble, France

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  4. Kengo Hirachi

    1. Graduate School of Mathematical Sciences, The University of Tokyo, Meguro-ku, Japan

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  5. Kang-Tae Kim

    1. Department of Mathematics, POSTECH, Pohang, Korea (Republic of)

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  6. Nikolay Shcherbina

    1. Department of Mathematics, Bergische Universität Wuppertal, Wuppertal, Germany

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  • Presents new advances in complex analysis and geometry
  • Contains contributions by top researchers in the field
  • Features several research problems for the future, including a chapter especially for this purpose
  • Includes supplementary material: sn.pub/extras

Part of the book series: Springer Proceedings in Mathematics & Statistics (PROMS, volume 144)

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Table of contents (28 papers)

  1. Front Matter

    Pages i-ix
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  2. Fatou Flowers and Parabolic Curves

    • Marco Abate
    Pages 1-39

  3. A CR Proof for a Global Estimate of the Diederich–Fornaess Index of Levi-Flat Real Hypersurfaces

    • Masanori Adachi
    Pages 41-48

  4. Unbounded Pseudoconvex Domains in \({\mathbb {C}}^n\) and Their Invariant Metrics

    • Taeyong Ahn, Hervé Gaussier, Kang-Tae Kim
    Pages 49-55

  5. Abstract Basins of Attraction

    • Leandro Arosio
    Pages 57-66

  6. Invertible Dynamics on Blow-ups of \({\mathbb {P}}^{k}\)

    • Eric Bedford
    Pages 67-88

  7. On Nazarov’s Complex Analytic Approach to the Mahler Conjecture and the Bourgain-Milman Inequality

    • Zbigniew Błocki
    Pages 89-98

  8. A Survey on Bergman Completeness

    • Bo-Yong Chen
    Pages 99-117

  9. Structure Theorems for Compact Kähler Manifolds with Nef Anticanonical Bundles

    • Jean-Pierre Demailly
    Pages 119-133

  10. An Estimate for the Squeezing Function and Estimates of Invariant Metrics

    • J. E. Fornæss, E. F. Wold
    Pages 135-147

  11. Classification of Proper Holomorphic Mappings Between Generalized Pseudoellipsoids of Different Dimensions

    • Atsushi Hayashimoto
    Pages 149-159

  12. Bergman Kernel Asymptotics and a Pure Analytic Proof of the Kodaira Embedding Theorem

    • Chin-Yu Hsiao
    Pages 161-173

  13. On the Density and the Volume Density Property

    • Shulim Kaliman, Frank Kutzschebauch
    Pages 175-186

  14. On Meromorphic Continuation of Local Zeta Functions

    • Joe Kamimoto, Toshihiro Nose
    Pages 187-195

  15. Themes on Non-analytic Singularities of Plurisubharmonic Functions

    • Dano Kim
    Pages 197-206

  16. Proper Holomorphic Maps Between Bounded Symmetric Domains

    • Sung-Yeon Kim
    Pages 207-219

  17. Characterizations of Strongly Pseudoconvex Models in Almost Complex and CR Geometries

    • Kang-Hyurk Lee
    Pages 221-233

  18. Compact Smooth but Non-complex Complements of Complete Kähler Manifolds

    • Xu Liu
    Pages 235-239

  19. Injectivity Theorems with Multiplier Ideal Sheaves and Their Applications

    • Shin-ichi Matsumura
    Pages 241-255

  20. Amoebas of Cuspidal Strata for Classical Discriminant

    • E. N. Mikhalkin, A. V. Shchuplev, A. K. Tsikh
    Pages 257-272
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Keywords

About this book

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.

Editors and Affiliations

  • Department of Mathematics, Università di Roma Tor Vergata, Rome, Italy

    Filippo Bracci

  • Dept. of Mathematics Education, Kyungnam University, Changwon, Korea (Republic of)

    Jisoo Byun

  • Université Joseph Fourier Grenoble, Institut Fourier, Grenoble, France

    Hervé Gaussier

  • Graduate School of Mathematical Sciences, The University of Tokyo, Meguro-ku, Japan

    Kengo Hirachi

  • Department of Mathematics, POSTECH, Pohang, Korea (Republic of)

    Kang-Tae Kim

  • Department of Mathematics, Bergische Universität Wuppertal, Wuppertal, Germany

    Nikolay Shcherbina

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