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Gromov’s Compactness Theorem for Pseudo-holomorphic Curves

  • Book
  • © 1997

Overview

Authors:
  1. Christoph Hummel

    1. Institut für Mathematik, Universität Zürich, Zürich, Switzerland
      Department of Mathematics, University of Pennsylvania, Philadelphia, USA

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Part of the book series: Progress in Mathematics (PM, volume 151)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-viii
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  2. Introduction

    • Christoph Hummel
    Pages 1-4

  3. Preliminaries

    • Christoph Hummel
    Pages 5-20

  4. Estimates for area and first derivatives

    • Christoph Hummel
    Pages 21-33

  5. Higher order derivatives

    • Christoph Hummel
    Pages 35-48

  6. Hyperbolic surfaces

    • Christoph Hummel
    Pages 49-77

  7. The compactness theorem

    • Christoph Hummel
    Pages 79-97

  8. The squeezing theorem

    • Christoph Hummel
    Pages 99-114

  9. Back Matter

    Pages 115-135
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Keywords

About this book

Mikhail Gromov introduced pseudo-holomorphic curves into symplectic geometry in 1985. Since then, pseudo-holomorphic curves have taken on great importance in many fields. The aim of this book is to present the original proof of Gromov's compactness theorem for pseudo-holomorphic curves in detail. Local properties of pseudo-holomorphic curves are investigated and proved from a geometric viewpoint. Properties of particular interest are isoperimetric inequalities, a monotonicity formula, gradient bounds and the removal of singularities. A special chapter is devoted to relevant features of hyperbolic surfaces, where pairs of pants decomposition and thickthin decomposition are described. The book is essentially self-contained and should also be accessible to students with a basic knowledge of differentiable manifolds and covering spaces.

Reviews

 
  "...the book provides a self-contained and for the most part excellent elaboration of Gromov's proof of the compactness theorem."   
  -- Mathematical Reviews 

Authors and Affiliations

  • Institut für Mathematik, Universität Zürich, Zürich, Switzerland

    Christoph Hummel

  • Department of Mathematics, University of Pennsylvania, Philadelphia, USA

    Christoph Hummel

Bibliographic Information

  • Book Title: Gromov’s Compactness Theorem for Pseudo-holomorphic Curves

  • Authors: Christoph Hummel

  • Series Title: Progress in Mathematics

  • DOI: https://doi.org/10.1007/978-3-0348-8952-0

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Basel 1997

  • Hardcover ISBN: 978-3-7643-5735-1Published: 01 May 1997

  • Softcover ISBN: 978-3-0348-9842-3Published: 15 October 2012

  • eBook ISBN: 978-3-0348-8952-0Published: 06 December 2012

  • Series ISSN: 0743-1643

  • Series E-ISSN: 2296-505X

  • Edition Number: 1

  • Number of Pages: VIII, 135

  • Topics: Geometry

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