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ABOUT THE BOOK

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

1. The Embedding Conjecture and the Approximation Conjecture in Higher Dimension

   • Matteo Fiacchi

   Pages 1-10

2. Fixed Points of Pseudo-Contractive Holomorphic Mappings

   • Mark Elin, David Shoikhet

   Pages 11-29

3. On Parabolic Dichotomy

   • Leandro Arosio

   Pages 31-42

4. Jordan Structures in Bounded Symmetric Domains

   • Cho-Ho Chu

   Pages 43-61

5. On Runge Neighborhoods of Closures of Domains Biholomorphic to a Ball

   • Hervé Gaussier, Cezar Joiţa

   Pages 63-66

6. Parametric Representations and Boundary Fixed Points of Univalent Self-Maps of the Unit Disk

   • Pavel Gumenyuk

   Pages 67-85

7. Is There a Teichmüller Principle in Higher Dimensions?

   • Oliver Roth

   Pages 87-105

8. Open Problems Related to a Herglotz-Type Formula for Vector-Valued Mappings

   • Jerry R. Muir Jr.

   Pages 107-115

9. Extremal Problems and Convergence Results for Mappings with Generalized Parametric Representation in ℂⁿ

   • Hidetaka Hamada, Mihai Iancu, Gabriela Kohr

   Pages 117-128

10. Open Problems and New Directions for p-Modulus on Networks

    • Nathan Albin, Pietro Poggi-Corradini

    Pages 129-141

11. Metric Properties of Domains in ℂⁿ

    • Hervé Gaussier

    Pages 143-155

12. On a Solution of a Particular Case of Aliaga-Tuneski Question

    • Dov Aharonov, Uri Elias

    Pages 157-163

13. Loewner Chains and Extremal Problems for Mappings with A-Parametric Representation in ℂⁿ

    • Ian Graham, Hidetaka Hamada, Gabriela Kohr, Mirela Kohr

    Pages 165-182