Holomorphic Curves and Global Questions in Contact Geometry

by Casim Abbas, Helmut Hofer

Overview

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.

Product Details

ISBN-13:	9783030118020
Publisher:	Springer International Publishing
Publication date:	03/30/2019
Series:	Birkhäuser Advanced Texts Basler Lehrbücher
Edition description:	1st ed. 2019
Pages:	322
Product dimensions:	6.10(w) x 9.25(h) x (d)

About the Author

Casim Abbas, Michigan State University, Michigan, USA
Helmut Hofer, Institute for Advanced Study, New Jersey, USA

Table of Contents

An Introduction to Contact Geometry.- Basic Results.- Surfaces in Three Dimensional Contact Manifolds.- Finite Energy Planes and Periodic Orbits.- Properties of Pseudoholomorphic Curves.- Intersection Theory for Pseudoholomorphic Disks.- Local Existence and Global Uniqueness Results.- Bubbling-off in Families of Pseudoholomorphic Disks.- Disk Filling Methods and Applications.

Editorial Reviews

The book under review is the entry point for studying low-dimensional foliations and the symplectic field theory. … It can be seen as a perfect tool for graduate students and researchers who would like to learn about pseudoholomorphic curves in contact geometry.” (Roman Golovko, zbMATH 1431.53001, 2020)

From the Publisher