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TitleHolomorphic Curves and Global Questions in Contact Geometry [electronic resource] / by Casim Abbas, Helmut Hofer
ImprintCham : Springer International Publishing : Imprint: Birkhäuser, 2019
Edition 1st ed. 2019
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Descript XII, 322 p. 33 illus., 2 illus. in color. online resource


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

Global differential geometry Global analysis Differentiable dynamical systems Differential equations partial Differential Geometry. Global Analysis and Analysis on Manifolds. Dynamical Systems and Ergodic Theory. Several Complex Variables and Analytic Spaces.


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