Advertisement

Holomorphic Curves and Global Questions in Contact Geometry

  • Casim Abbas
  • Helmut Hofer
Textbook
  • 3.8k Downloads

Part of the Birkhäuser Advanced Texts Basler Lehrbücher book series (BAT)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Casim Abbas, Helmut Hofer
    Pages 1-23
  3. Casim Abbas, Helmut Hofer
    Pages 25-51
  4. Casim Abbas, Helmut Hofer
    Pages 53-96
  5. Casim Abbas, Helmut Hofer
    Pages 97-120
  6. Casim Abbas, Helmut Hofer
    Pages 121-147
  7. Casim Abbas, Helmut Hofer
    Pages 149-199
  8. Casim Abbas, Helmut Hofer
    Pages 201-244
  9. Casim Abbas, Helmut Hofer
    Pages 245-258
  10. Casim Abbas, Helmut Hofer
    Pages 259-265
  11. Back Matter
    Pages 267-322

About this book

Introduction

This book explains the foundations of holomorphic curve theory in contact geometry. By using a particular geometric problem as a starting point the authors guide the reader into the subject. As such it ideally serves as preparation and as entry point for a deeper study of the analysis underlying symplectic field theory.

An introductory chapter sets the stage explaining some of the basic notions of contact geometry and the role of holomorphic curves in the field. The authors proceed to the heart of the material providing a detailed exposition about finite energy planes and periodic orbits (chapter 4) to disk filling methods and applications (chapter 9).

The material is self-contained. It includes a number of technical appendices giving the geometric analysis foundations for the main results, so that one may easily follow the discussion. Graduate students as well as researchers who want to learn the basics of this fast developing theory will highly appreciate this accessible approach taken by the authors.

Keywords

finite energy planes weinstein conjecture pseudoholomorphic curves disk filling method contact forms contact structures reeb vector fields

Authors and affiliations

  • Casim Abbas
    • 1
  • Helmut Hofer
    • 2
  1. 1.Michigan State UniversityEast LansingUSA
  2. 2.Institute for Advanced StudyPrincetonUSA

Bibliographic information