Holomorphic Curves and Global Questions in Contact Geometry

• Κύριοι συγγραφείς: Abbas, Casim (Συγγραφέας, http://id.loc.gov/vocabulary/relators/aut), Hofer, Helmut (http://id.loc.gov/vocabulary/relators/aut)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Birkhäuser, 2019.
• Έκδοση: 1st ed. 2019.
• Σειρά: Birkhäuser Advanced Texts Basler Lehrbücher,
• Θέματα: Differential geometry.; Global analysis (Mathematics).; Manifolds (Mathematics).; Dynamics.; Ergodic theory.; Functions of complex variables.; Differential Geometry.; Global Analysis and Analysis on Manifolds.; Dynamical Systems and Ergodic Theory.; Several Complex Variables and Analytic Spaces.

 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. 

 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.