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© 1997

Gromov’s Compactness Theorem for Pseudo-holomorphic Curves

Book

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

Table of contents

  1. Front Matter
    Pages i-viii
  2. Christoph Hummel
    Pages 1-4
  3. Christoph Hummel
    Pages 5-20
  4. Christoph Hummel
    Pages 21-33
  5. Christoph Hummel
    Pages 35-48
  6. Christoph Hummel
    Pages 49-77
  7. Christoph Hummel
    Pages 79-97
  8. Christoph Hummel
    Pages 99-114
  9. Back Matter
    Pages 115-135

About this book

Introduction

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.

Keywords

geometry manifold proof symplectic geometry theorem

Authors and affiliations

  1. 1.Institut für MathematikUniversität ZürichZürichSwitzerland
  2. 2.Department of MathematicsUniversity of PennsylvaniaPhiladelphiaUSA

Bibliographic information

  • Book Title Gromov’s Compactness Theorem for Pseudo-holomorphic Curves
  • Authors Christoph Hummel
  • Series Title Progress in Mathematics
  • Series Abbreviated Title Progress in Mathematics(Birkhäuser)
  • DOI https://doi.org/10.1007/978-3-0348-8952-0
  • Copyright Information Birkhäuser Verlag Basel Switzerland 1997
  • Publisher Name Birkhäuser, Basel
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-3-7643-5735-1
  • Softcover ISBN 978-3-0348-9842-3
  • eBook ISBN 978-3-0348-8952-0
  • Series ISSN 0743-1643
  • Series E-ISSN 2296-505X
  • Edition Number 1
  • Number of Pages VIII, 135
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Geometry
  • Buy this book on publisher's site

Reviews

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