Holomorphic Curves and Global Questions in Contact Geometry

Download or read book Holomorphic Curves and Global Questions in Contact Geometry written by Casim Abbas and published by Birkhäuser. This book was released on 2019-04-14 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.