Abbas / Hofer Holomorphic Curves and Global Questions in Contact Geometry

Erscheinungsjahr 2019
ISBN: 978-3-030-11803-7
Verlag: Springer International Publishing
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 322 Seiten, eBook

Reihe: Birkhäuser Advanced Texts Basler Lehrbücher

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.

Zielgruppe

Graduate

Autoren/Hrsg.

Abbas, Casim

Hofer, Helmut

Inhaltsverzeichnis

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.

Über Autor(innen)

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