© 2011

Stein Manifolds and Holomorphic Mappings

The Homotopy Principle in Complex Analysis

  • First systematic presentation of the theory of holomorphic automorphisms of complex Euclidean spaces

  • First complete account of Oka-Grauert theory and its modern extensions

  • Contains a wide variety of applications ranging from classical to contemporary


Table of contents

  1. Front Matter
    Pages I-XII
  2. Franc Forstnerič
    Pages 1-42
  3. Franc Forstnerič
    Pages 43-56
  4. Franc Forstnerič
    Pages 99-184
  5. Franc Forstnerič
    Pages 185-240
  6. Franc Forstnerič
    Pages 241-290
  7. Franc Forstnerič
    Pages 291-332
  8. Franc Forstnerič
    Pages 333-400
  9. Franc Forstnerič
    Pages 401-460
  10. Back Matter
    Pages 461-489

About this book


The main theme of this book is the homotopy principle for holomorphic mappings from Stein manifolds to the newly introduced class of Oka manifolds. The book contains the first complete account of Oka-Grauert theory and its modern extensions, initiated by Mikhail Gromov and developed in the last decade by the author and his collaborators. Included is the first systematic presentation  of the theory of holomorphic automorphisms of complex Euclidean spaces, a survey on Stein neighborhoods, connections between the geometry of Stein surfaces and Seiberg-Witten theory, and a wide variety of applications ranging from classical to contemporary.


Holomorphic approximation Oka manifolds Stein manifolds Stein spaces

Authors and affiliations

  1. 1.Faculty of Mathematics and PhysicsUniversity of LjubljanaLjubljanaSlovenia

About the authors

Franc Forstneric has published close to eighty research and survey papers in complex analysis and geometry, including several in leading mathematical journals such as the Annals of Math., Acta Math., Inventiones Math., Duke Math. J., Amer. J. Math., Math. Ann., and others.

He held long term teaching and research positions at the

University of Wisconsin-Madison (Madison, USA),

Institut Mittag-Leffler (Stockholm, Sweden),

Max Planck Institute (Bonn, Germany),

as well as visiting positions at more than ten other institutions.  He was an invited speaker at over 70 international conferences and workshops.

Since 2000 he is a Professor of Mathematics at the University of Ljubljana and is a member of the Academy of Sciences of the Republic of Slovenia

Bibliographic information

  • Book Title Stein Manifolds and Holomorphic Mappings
  • Book Subtitle The Homotopy Principle in Complex Analysis
  • Authors Franc Forstnerič
  • Series Title Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 2011
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-3-642-22249-8
  • Softcover ISBN 978-3-642-27032-1
  • eBook ISBN 978-3-642-22250-4
  • Series ISSN 0071-1136
  • Edition Number 1
  • Number of Pages XII, 492
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Real Functions
    Functions of a Complex Variable
  • Buy this book on publisher's site


From the reviews:

“The main focus of the book is the theory of the Oka principle, which has been extensively developed in the past decade following a seminal paper of Gromov in 1989. … The book can serve as a textbook for advanced graduate students specialising in complex geometry, as a reference for researchers in the field, and as an accessible resource for people in related areas. The book truly fills a gap in the literature. … a standard reference for years to come.” (Finnur Lárusson, Mathematical Reviews, May, 2013)