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Geometric Function Theory in Higher Dimension

  • Book
  • © 2017

Overview

Editors:
  1. Filippo Bracci

    1. Dipartimento di Matematica, Università di Roma Tor Vergata, Rome, Italy

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  • Includes contributions from leading international researchers in the area
  • Offers a survey of challenging open problems in this field
  • Provides deep insights into new connections between different areas of research

Part of the book series: Springer INdAM Series (SINDAMS, volume 26)

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Table of contents (13 chapters)

  1. Front Matter

    Pages i-xi
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  2. The Embedding Conjecture and the Approximation Conjecture in Higher Dimension

    • Matteo Fiacchi
    Pages 1-10

  3. Fixed Points of Pseudo-Contractive Holomorphic Mappings

    • Mark Elin, David Shoikhet
    Pages 11-29

  4. On Parabolic Dichotomy

    • Leandro Arosio
    Pages 31-42

  5. Jordan Structures in Bounded Symmetric Domains

    • Cho-Ho Chu
    Pages 43-61

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

    • Hervé Gaussier, Cezar Joiţa
    Pages 63-66

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

    • Pavel Gumenyuk
    Pages 67-85

  8. Is There a Teichmüller Principle in Higher Dimensions?

    • Oliver Roth
    Pages 87-105

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

    • Jerry R. Muir Jr.
    Pages 107-115

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

    • Hidetaka Hamada, Mihai Iancu, Gabriela Kohr
    Pages 117-128

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

    • Nathan Albin, Pietro Poggi-Corradini
    Pages 129-141

  12. Metric Properties of Domains in ℂn

    • Hervé Gaussier
    Pages 143-155

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

    • Dov Aharonov, Uri Elias
    Pages 157-163

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

    • Ian Graham, Hidetaka Hamada, Gabriela Kohr, Mirela Kohr
    Pages 165-182
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Keywords

About this 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.

Editors and Affiliations

  • Dipartimento di Matematica, Università di Roma Tor Vergata, Rome, Italy

    Filippo Bracci

About the editor

Prof. Filippo Bracci obtained his Ph.D. in Mathematics at the University of Padova in 2001. He is currently full professor at Università di Roma “Tor Vergata”. He was the principal investigator of the ERC project “HEVO”. His research interests include complex analysis, several complex variables, and holomorphic dynamics.

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