Metrical and Dynamical Aspects in Complex Analysis

Description

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. Front Matter ....Pages i-xiv Invariant Distances (Marco Abate)....Pages 1-24 Dynamics in Several Complex Variables (Marco Abate)....Pages 25-54 Gromov Hyperbolic Spaces and Applications to Complex Analysis (Hervé Pajot)....Pages 55-66 Gromov Hyperbolicity of Bounded Convex Domains (Andrew Zimmer)....Pages 67-114 Quasi-Conformal Mappings (Hervé Pajot)....Pages 115-140 Carleson Measures and Toeplitz Operators (Marco Abate)....Pages 141-157 Back Matter ....Pages 159-173