Geometric Function Theory in Higher Dimension

✍ Scribed by Filippo Bracci

• Publisher: Springer International Publishing
• Year: 2017
• Tongue: English
• Leaves: 185
• Series: Springer INdAM Series 26
• Edition: 1st ed.
• Category: Library

✦ Synopsis

The book collects the most relevant outcomes from the INdAM Workshop “Geometric Function Theory in Higher Dimension” held in Cortona on September 5-9, 2016. The Workshop was mainly devoted to discussions of basic open problems in the area, and this volume follows the same line. In particular, it offers a selection of original contributions on Loewner theory in one and higher dimensions, semigroups theory, iteration theory and related topics. Written by experts in geometric function theory in one and several complex variables, it focuses on new research frontiers in this area and on challenging open problems. The book is intended for graduate students and researchers working in complex analysis, several complex variables and geometric function theory.

✦ Table of Contents

Front Matter ....Pages i-xi
The Embedding Conjecture and the Approximation Conjecture in Higher Dimension (Matteo Fiacchi)....Pages 1-10
Fixed Points of Pseudo-Contractive Holomorphic Mappings (Mark Elin, David Shoikhet)....Pages 11-29
On Parabolic Dichotomy (Leandro Arosio)....Pages 31-42
Jordan Structures in Bounded Symmetric Domains (Cho-Ho Chu)....Pages 43-61
On Runge Neighborhoods of Closures of Domains Biholomorphic to a Ball (Hervé Gaussier, Cezar Joiţa)....Pages 63-66
Parametric Representations and Boundary Fixed Points of Univalent Self-Maps of the Unit Disk (Pavel Gumenyuk)....Pages 67-85
Is There a Teichmüller Principle in Higher Dimensions? (Oliver Roth)....Pages 87-105
Open Problems Related to a Herglotz-Type Formula for Vector-Valued Mappings (Jerry R. Muir Jr.)....Pages 107-115
Extremal Problems and Convergence Results for Mappings with Generalized Parametric Representation in ℂn (Hidetaka Hamada, Mihai Iancu, Gabriela Kohr)....Pages 117-128
Open Problems and New Directions for p-Modulus on Networks (Nathan Albin, Pietro Poggi-Corradini)....Pages 129-141
Metric Properties of Domains in ℂn (Hervé Gaussier)....Pages 143-155
On a Solution of a Particular Case of Aliaga-Tuneski Question (Dov Aharonov, Uri Elias)....Pages 157-163
Loewner Chains and Extremal Problems for Mappings with A-Parametric Representation in ℂn (Ian Graham, Hidetaka Hamada, Gabriela Kohr, Mirela Kohr)....Pages 165-182

✦ Subjects

Mathematics; Several Complex Variables and Analytic Spaces; Functions of a Complex Variable; Functional Analysis; Dynamical Systems and Ergodic Theory