Metrical and Dynamical Aspects in Complex Analysis

The central theme of this reference book is the metric geometry of complex analysis in several variables. Bridging a gap in the current literature, the text focuses on the fine behavior of the Kobayashi metric of complex manifolds and its relationships to dynamical systems, hyperbolicity in the sense of Gromov and operator theory, all very active areas of research. The modern points of view expressed in these notes, collected here for the first time, will be of interest to academics working in the fields of several complex variables and metric geometry. The different topics are treated coherently and include expository presentations of the relevant tools, techniques and objects, which will be particularly useful for graduate and PhD students specializing in the area.

List of contents

1. Invariant Distances.- 2. Dynamics in Several Complex Variables.- 3. Gromov Hyperbolic Spaces and Applications to Complex Analysis.- 4. Gromov Hyperbolicity of Bounded Convex Domains.- 5. Quasi-conformal Mappings.- 6. Carleson Measures and Toeplitz Operators. References.

Summary

Offers a new point of view on geometric complex analysis
Collects together notes in several very active areas of research

Includes expository presentations and numerous applications

Product details

• Assisted by: Léa Blanc-Centi (Editor)
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 04.11.2017
• EAN: 9783319658360
• ISBN: 978-3-31-965836-0
• No. of pages: 173
• Dimensions: 152 mm x 236 mm x 12 mm
• Weight: 308 g
• Illustrations: XIV, 173 p.
• Series: Lecture Notes in Mathematics
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Analysis; B, Dynamics, Mathematics and Statistics, Dynamical Systems and Ergodic Theory, Ergodic theory, Nonlinear science, Dynamical systems, Functions of complex variables, Several Complex Variables and Analytic Spaces, Hyperbolic Geometry, Non-Euclidean geometry