1.

Record Nr.

UNINA9910338256203321

Autore

Abbas Casim

Titolo

Holomorphic Curves and Global Questions in Contact Geometry / / by Casim Abbas, Helmut Hofer

Pubbl/distr/stampa

Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2019

ISBN

3-030-11803-7

Edizione

[1st ed. 2019.]

Descrizione fisica

1 online resource (XII, 322 p. 33 illus., 2 illus. in color.)

Collana

Birkhäuser Advanced Texts Basler Lehrbücher, , 2296-4894

Disciplina

515.98

Soggetti

Geometry, Differential

Global analysis (Mathematics)

Manifolds (Mathematics)

Dynamics

Functions of complex variables

Differential Geometry

Global Analysis and Analysis on Manifolds

Dynamical Systems

Several Complex Variables and Analytic Spaces

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Nota di contenuto

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.

Sommario/riassunto

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.