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The Bergman Kernel and Related Topics

Hayama Symposium on SCV XXIII, Kanagawa, Japan, July 2022

  • Conference proceedings
  • © 2024

Overview

  • Covers most area of the Bergman Kernel theory in complex analysis/geometry
  • Most of the authors are well-known experts who created the theory
  • Introductory surveys and research articles are both included

Part of the book series: Springer Proceedings in Mathematics & Statistics (PROMS, volume 447)

Included in the following conference series:

Conference proceedings info: HSSCV 2022.

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Table of contents (15 papers)

Other volumes

  1. The Bergman Kernel and Related Topics

Keywords

About this book

This volume consists of 15 papers contributing to the Hayama Symposium on Complex Analysis in Several Variables XXIII, which was dedicated to the 100th anniversary of the creation of the Bergman kernel. The symposium took place in Hayama and Tokyo in July 2022. Each article is closely related to the Bergman kernel, covering topics in complex analysis, differential geometry, representation theory, PDE, operator theory, and complex algebraic geometry.

Specifically, some papers address the L2 extension operators from a newly opened viewpoint after solving Suita's conjecture for the logarithmic capacity. They are also continuations of quantitative solutions to the openness conjecture for the multiplier ideal sheaves. The study involves estimates for the solutions of the d-bar equations, focusing on the existence of compact Levi-flat hypersurfaces in complex manifolds.

The collection also reports progress on various topics, including the existence of extremal Kähler metrics on compact manifolds, Lp variants of the Bergman kernel, Wehrl-type inequalities, homogeneous Kähler metrics on bounded homogeneous domains, asymptotics of the Bergman kernels, and harmonic Szegő kernels and operators on the Bergman spaces and Segal-Bargmann spaces.

Some of the papers are written in an easily accessible way for beginners. Overall, this collection updates how a basic notion provides strong insights into the internal relationships between independently found phenomena.

Editors and Affiliations

  • Graduate School of Mathematical Sciences, The University of Tokyo, Tokyo, Japan

    Kengo Hirachi, Shigeharu Takayama

  • Graduate School of Mathematics, Nagoya University, Nagoya, Japan

    Takeo Ohsawa

  • Faculty of Mathematics, Kyushu University, Fukuoka, Japan

    Joe Kamimoto

About the editors

Professor Kengo Hirachi is a full professor at the University of Tokyo and awarded the 2006 Bergman prize. Aldo he was an invited speaker of ICM 2014 (analysis section).

Professor Takeo Ohsawa is a professor emeritus of Nagoya University. He was also an invited speaker of ICM 1990. 

Professor Shigeharu Takayama is a full professor of the University of Tokyo. 

Professor Joe Kamimoto is a full professor of Kyushu University. 

Bibliographic Information

  • Book Title: The Bergman Kernel and Related Topics

  • Book Subtitle: Hayama Symposium on SCV XXIII, Kanagawa, Japan, July 2022

  • Editors: Kengo Hirachi, Takeo Ohsawa, Shigeharu Takayama, Joe Kamimoto

  • Series Title: Springer Proceedings in Mathematics & Statistics

  • DOI: https://doi.org/10.1007/978-981-99-9506-6

  • Publisher: Springer Singapore

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024

  • Hardcover ISBN: 978-981-99-9505-9Published: 20 March 2024

  • Softcover ISBN: 978-981-99-9508-0Due: 20 April 2024

  • eBook ISBN: 978-981-99-9506-6Published: 19 March 2024

  • Series ISSN: 2194-1009

  • Series E-ISSN: 2194-1017

  • Edition Number: 1

  • Number of Pages: VIII, 369

  • Number of Illustrations: 4 b/w illustrations

  • Topics: Several Complex Variables and Analytic Spaces, Differential Geometry, Algebraic Geometry

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