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Holomorphic curves and global questi...

Abbas, Casim.

Holomorphic curves and global questions in contact geometry

Record Type:	Electronic resources : Monograph/item
Title/Author:	Holomorphic curves and global questions in contact geometryby Casim Abbas, Helmut Hofer.
Author:	Abbas, Casim.
other author:	Hofer, Helmut.
Published:	Cham :Springer International Publishing :2019.
Description:	xii, 322 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Holomorphic functions.
Online resource:	https://doi.org/10.1007/978-3-030-11803-7
ISBN:	9783030118037$q(electronic bk.)

Holomorphic curves and global questions in contact geometry
Abbas, Casim.

Holomorphic curves and global questions in contact geometry[electronic resource] /by Casim Abbas, Helmut Hofer. - Cham :Springer International Publishing :2019. - xii, 322 p. :ill., digital ;24 cm. - Birkhauser advanced texts basler lehrbucher,1019-6242. - Birkhauser advanced texts basler lehrbucher..

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.

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.

ISBN: 9783030118037$q(electronic bk.)

Standard No.: 10.1007/978-3-030-11803-7doiSubjects--Topical Terms:

275778
Holomorphic functions.

LC Class. No.: QA331 / .A23 2019

Dewey Class. No.: 515.98

Holomorphic curves and global questions in contact geometry
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245 1 0 $a Holomorphic curves and global questions in contact geometry $h [electronic resource] / $c by Casim Abbas, Helmut Hofer.
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490 1 $a Birkhauser advanced texts basler lehrbucher, $x 1019-6242
505 0 $a 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.
520 $a 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.
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650 1 4 $a Differential Geometry. $3 273785
650 2 4 $a Global Analysis and Analysis on Manifolds. $3 273786
650 2 4 $a Dynamical Systems and Ergodic Theory. $3 273794
650 2 4 $a Several Complex Variables and Analytic Spaces. $3 276692
700 1 $a Hofer, Helmut. $3 836560
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