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.-- From back cover 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 The book collects the most relevant outcomes from the INdAM Workshop zGeometric Function Theory in Higher Dimensiony 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
