Skip to main content
SpringerLink
Log in
Book cover

Theory of Stein Spaces

  • Book
  • © 1979

Overview

Authors:
  1. Hans Grauert

    1. Mathematisches Institut, Universität Göttingen, Göttingen, Federal Republic of Germany

    View author publications

    You can also search for this author in PubMed   Google Scholar

  2. Reinhold Remmert

    1. Mathematisches Institut, Westfälischen Wilhelms-Universität, Münster, Federal Republic of Germany

    View author publications

    You can also search for this author in PubMed   Google Scholar

Part of the book series: Grundlehren der mathematischen Wissenschaften (GL, volume 236)

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 74.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (9 chapters)

  1. Front Matter

    Pages I-XXI
    Download chapter PDF

  2. Sheaf Theory

    • Hans Grauert, Reinhold Remmert
    Pages 1-27

  3. Cohomology Theory

    • Hans Grauert, Reinhold Remmert
    Pages 28-44

  4. Coherence Theory for Finite Holomorphic Maps

    • Hans Grauert, Reinhold Remmert
    Pages 45-55

  5. Differential Forms and Dolbeault Theory

    • Hans Grauert, Reinhold Remmert
    Pages 56-82

  6. Theorems A and B for Compact Blocks in ℂm

    • Hans Grauert, Reinhold Remmert
    Pages 83-99

  7. Stein Spaces

    • Hans Grauert, Reinhold Remmert
    Pages 100-124

  8. Applications of Theorems A and B

    • Hans Grauert, Reinhold Remmert
    Pages 125-185

  9. The Finiteness Theorem

    • Hans Grauert, Reinhold Remmert
    Pages 186-203

  10. Compact Riemann Surfaces

    • Hans Grauert, Reinhold Remmert
    Pages 204-239

  11. Back Matter

    Pages 240-252
    Download chapter PDF
Back to top

Keywords

About this book

1. The classical theorem of Mittag-Leffler was generalized to the case of several complex variables by Cousin in 1895. In its one variable version this says that, if one prescribes the principal parts of a merom orphic function on a domain in the complex plane e, then there exists a meromorphic function defined on that domain having exactly those principal parts. Cousin and subsequent authors could only prove the analogous theorem in several variables for certain types of domains (e. g. product domains where each factor is a domain in the complex plane). In fact it turned out that this problem can not be solved on an arbitrary domain in em, m ~ 2. The best known example for this is a "notched" bicylinder in 2 2 e . This is obtained by removing the set { (z , z ) E e 11 z I ~ !, I z 1 ~ !}, from 1 2 1 2 2 the unit bicylinder, ~ :={(z , z ) E e llz1 < 1, lz1 < 1}. This domain D has 1 2 1 2 the property that every function holomorphic on D continues to a function holo­ morphic on the entire bicylinder. Such a phenomenon never occurs in the theory of one complex variable. In fact, given a domain G c e, there exist functions holomorphic on G which are singular at every boundary point of G.

Authors and Affiliations

  • Mathematisches Institut, Universität Göttingen, Göttingen, Federal Republic of Germany

    Hans Grauert

  • Mathematisches Institut, Westfälischen Wilhelms-Universität, Münster, Federal Republic of Germany

    Reinhold Remmert

Bibliographic Information

  • Book Title: Theory of Stein Spaces

  • Authors: Hans Grauert, Reinhold Remmert

  • Series Title: Grundlehren der mathematischen Wissenschaften

  • DOI: https://doi.org/10.1007/978-1-4757-4357-9

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1979

  • eBook ISBN: 978-1-4757-4357-9Published: 14 March 2013

  • Series ISSN: 0072-7830

  • Series E-ISSN: 2196-9701

  • Edition Number: 1

  • Number of Pages: XXI, 252

  • Number of Illustrations: 2 b/w illustrations

  • Additional Information: Original German edition published as volume 227 in the same series

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

Publish with us

Policies and ethics

Back to top

Search

Navigation