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This book provides an introduction to symplectic field theory, a new and important subject which is currently being developed. The starting point of this theory are compactness results for holomorphic curves established in the last decade. The author presents a systematic introduction providing a lot of background material, much of which is scattered throughout the literature. Since the content grew out of lectures given by the author, the main aim is to provide an entry point into symplectic field theory for non-specialists and for graduate students. Extensions of certain compactness results, which are believed to be true by the specialists but have not yet been published in the literature in detail, top off the scope of this monograph.

Cell aggregation_xMathematics. --- Field theory (Physics) -- Congresses. --- Global differential geometry. --- Mathematics. --- Symplectic geometry -- Congresses. --- Symplectic geometry. --- Symplectic manifolds -- Congresses. --- Symplectic geometry --- Mathematics --- Physical Sciences & Mathematics --- Geometry --- Differential geometry. --- Manifolds (Mathematics). --- Complex manifolds. --- Differential Geometry. --- Manifolds and Cell Complexes (incl. Diff.Topology). --- Geometry, Differential --- Cell aggregation --- Aggregation, Cell --- Cell patterning --- Cell interaction --- Microbial aggregation --- Analytic spaces --- Manifolds (Mathematics) --- Topology --- Differential geometry

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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.

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. --- Partial differential equations --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Geometry, Differential --- Holomorphic functions. --- Symplectic geometry. --- Functions, Holomorphic --- Functions of several complex variables --- Differential geometry. --- Global analysis (Mathematics). --- Manifolds (Mathematics). --- Dynamics. --- Ergodic theory. --- Functions of complex variables. --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Topology --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Differential geometry --- Complex variables --- Elliptic functions --- Functions of real variables --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Geometry, Differential. --- Dynamical systems. --- Dynamical Systems.

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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.

Geometry, Differential. --- Global analysis (Mathematics) --- Manifolds (Mathematics) --- Dynamics. --- Ergodic theory. --- Functions of complex variables.