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Geometry and Analysis on Manifolds

In Memory of Professor Shoshichi Kobayashi

  • Book
  • © 2015

Overview

Editors:
  1. Takushiro Ochiai

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

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  2. Toshiki Mabuchi

    1. Department of Mathematics, Osaka University Graduate School of Sciences, Osaka, Japan

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  3. Yoshiaki Maeda

    1. Tohoku Forum for Creativity, Tohoku University, Yokohama, Japan

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  4. Junjiro Noguchi

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

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  5. Alan Weinstein

    1. Department of Mathematics University of California at Berkeley, Berkeley, USA

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  • Presents lectures on recent topics in complex geometry and complex analysis for young researchers
  • Broadens your insight on merging geometry and analysis on manifolds
  • Provides a comprehensive list of Shoshichi Kobayashi’s publications and academic genealogy
  • Features authoritative papers

Part of the book series: Progress in Mathematics (PM, volume 308)

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Table of contents (21 chapters)

  1. Front Matter

    Pages i-viii
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  2. About Shoshichi Kobayashi

    1. Front Matter

      Pages 1-1
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    2. In Memory of Professor Shoshichi Kobayashi

      • Takushiro Ochiai
      Pages 3-12

    3. Events Surrounding the Birth of the Kobayashi Metric

      • Hung-Hsi Wu
      Pages 13-15

    4. Academic Genealogy of Shoshichi Kobayashi and Individuals Who Influenced Him

      • Hisashi Kobayashi
      Pages 17-38

  3. Algebraic Geometry and Complex Analysis

    1. Front Matter

      Pages 39-39
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    2. Algebraic Differential Equations for Entire Holomorphic Curves in Projective Hypersurfaces of General Type: Optimal Lower Degree Bound

      • Joël Merker
      Pages 41-142

    3. Kobayashi Hyperbolicity and Lang’s Conjecture

      • Junjiro Noguchi
      Pages 143-151

    4. A Lemma on Hartogs Function and Application to Levi Flat Hypersurfaces in Hopf Surfaces

      • Takeo Ohsawa
      Pages 153-157

    5. On the Extremal Measure on a Complex Manifold

      • Hajime Tsuji
      Pages 159-175

    6. A Lang Exceptional Set for Integral Points

      • Paul Vojta
      Pages 177-207

    7. Kobayashi Hyperbolicity and Higher-dimensional Nevanlinna Theory

      • Katsutoshi Yamanoi
      Pages 209-273

    8. Geometry and Arithmetic on the Siegel–Jacobi Space

      • Jae-Hyun Yang
      Pages 275-325

    9. On the Pseudonorm Project of Birational Classification of Algebraic Varieties

      • Shing-Tung Yau
      Pages 327-339

  4. Differential Geometry

    1. Front Matter

      Pages 341-341
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    2. The Weighted Laplacians on Real and Complex Metric Measure Spaces

      • Akito Futaki
      Pages 343-351

    3. Locally Conformally Kähler Structures on Homogeneous Spaces

      • Keizo Hasegawa, Yoshinobu Kamishima
      Pages 353-372

    4. A Note on Vanishing Theorems

      • Nigel Hitchin
      Pages 373-382

    5. Dupin Hypersurfaces in Lie Sphere Geometry

      • Gary R. Jensen
      Pages 383-394

    6. The Donaldson–Futaki Invariant for Sequences of Test Configurations

      • Toshiki Mabuchi
      Pages 395-403
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Keywords

About this book

This volume is dedicated to the memory of Shoshichi Kobayashi, and gathers contributions from distinguished researchers working on topics close to his research areas. The book is organized into three parts, with the first part presenting an overview of Professor Shoshichi Kobayashi’s career. This is followed by two expository course lectures (the second part) on recent topics in extremal Kähler metrics and value distribution theory, which will be helpful for graduate students in mathematics interested in new topics in complex geometry and complex analysis. Lastly, the third part of the volume collects authoritative research papers on differential geometry and complex analysis.

Professor Shoshichi Kobayashi was a recognized international leader in the areas of differential and complex geometry. He contributed crucial ideas that are still considered fundamental in these fields. The book will be of interest to researchers in the fields of differential geometry, complex geometry, and several complex variables geometry, as well as to graduate students in mathematics.

Editors and Affiliations

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

    Takushiro Ochiai, Junjiro Noguchi

  • Department of Mathematics, Osaka University Graduate School of Sciences, Osaka, Japan

    Toshiki Mabuchi

  • Tohoku Forum for Creativity, Tohoku University, Yokohama, Japan

    Yoshiaki Maeda

  • Department of Mathematics University of California at Berkeley, Berkeley, USA

    Alan Weinstein

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