Geometric Function Theory in Higher Dimension

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.

1 Matteo Fiacchi, The Embedding Conjecture and the Approximation Conjecture in Higher Dimension.- 2 Mark Elin and David Shoikhet, Fixed Points of Pseudo-Contractive Holomorphic Mappings.- 3 Leandro Arosio, On Parabolic Dichomoty.- 4 Cho-Ho Chu, Jordan Structures in Bounded Symmetric Domains.- 5 Hervé Gaussier and Cezar Joita, On Runge Neighborhoods of Closures of Domains Biholomorphic to a Ball.- 6 Pavel Gumenyuk, Parametric Representations and Boundary Fixed Points of Univalent Self-Maps of the Unit Disk.- 7 Oliver Roth, Is there a Teichmuller principle in higher dimensions?.- 8 Jerry R. Muir Jr., Open Problems Related to a Herglotz-Type Formula for Vector-Valued Mappings.- 9 Hidetaka Hamada et al., Extremal Problems and Convergence Results for Mappings with Generalized Parametric Representation in Cn.- 10 Nathan Albin and Pietro Poggi-Corradini, Open Problems and New Directions for p-Modulus on Networks.- 11 Hervé Gaussier, Metric Properties of Domains in Cn.- 12 Dov Aharonov andU. Elias, On a Solution of a Particular Case of Aliaga-Tuneski Question.- 13 Ian Graham et al., Loewner Chains and Extremal Problems for Mappings with A-Parametric Representation Cn.