© 1998

Hyperbolic Complex Spaces


Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 318)

Table of contents

  1. Front Matter
    Pages I-XIII
  2. Shoshichi Kobayashi
    Pages 1-17
  3. Shoshichi Kobayashi
    Pages 19-47
  4. Shoshichi Kobayashi
    Pages 49-171
  5. Shoshichi Kobayashi
    Pages 173-237
  6. Shoshichi Kobayashi
    Pages 239-275
  7. Shoshichi Kobayashi
    Pages 277-341
  8. Shoshichi Kobayashi
    Pages 343-392
  9. Shoshichi Kobayashi
    Pages 393-428
  10. Back Matter
    Pages 429-474

About this book


In the three decades since the introduction of the Kobayashi distance, the subject of hyperbolic complex spaces and holomorphic mappings has grown to be a big industry. This book gives a comprehensive and systematic account on the Carathéodory and Kobayashi distances, hyperbolic complex spaces and holomorphic mappings with geometric methods. A very complete list of references should be useful for prospective researchers in this area.


Hyperbolische komplexe Räume Schwarz lemma curvature holomorphe Abbildungen holomorphic mappings hyperbolic complex spaces intrinsic distances manifold

Authors and affiliations

  1. 1.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

Bibliographic information

  • Book Title Hyperbolic Complex Spaces
  • Authors Shoshichi Kobayashi
  • Series Title Grundlehren der mathematischen Wissenschaften
  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 1998
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-3-540-63534-5
  • Softcover ISBN 978-3-642-08339-6
  • eBook ISBN 978-3-662-03582-5
  • Series ISSN 0072-7830
  • Edition Number 1
  • Number of Pages XIV, 474
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Differential Geometry
    Several Complex Variables and Analytic Spaces
  • Buy this book on publisher's site


"The author's book is exceptionally well organized, with an impressive collection of references to the literature. A particular strength of the book is the author's taste in choosing which examples to include and which to omit. The author did an excellent job of selecting and treating examples that are essential for developing the reader's intuition about the subject and contented himself with citing the literature for technical examples that illustrate finer points. Although the index is quite good for locating the definitions of all the important terms, the one fault this reviewer found with the book is that because the book has so many things in it, he felt that a more comprehensive index including entries such as "complete hyperbolic implies taut, page 240" was in order. This reviewer would recommend this book to nearly anyone interested in the geometry and function theory of complex manifolds, although a beginning student may find some of the later chapters a little rough going at times."--MATHEMATICAL REVIEWS