© 1997

Gromov’s Compactness Theorem for Pseudo-holomorphic Curves


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


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.


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
  • 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


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