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Frontiers in Mathematics

Schwarz-Pick Type Inequalities

Authors: Avkhadiev, Farit G., Wirths, Karl-Joachim

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  • Contains historical remarks on the Schwarz Lemma as well as new theorems on Schwarz-Pick inequalities from the last 25 years
  • Features several analytic methods as well as interesting applications of geometric properties of domains from very special cases to domains with uniformly perfect boundary
  • Details many open problems, old and new, in geometric function theory
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About this book

This book discusses in detail the extension of the Schwarz-Pick inequality to higher order derivatives of analytic functions with given images. It is the first systematic account of the main results in this area. Recent results in geometric function theory presented here include the attractive steps on coefficient problems from Bieberbach to de Branges, applications of some hyperbolic characteristics of domains via Beardon-Pommerenke's theorem, a new interpretation of coefficient estimates as certain properties of the Poincaré metric, and a successful combination of the classical ideas of Littlewood, Löwner and Teichmüller with modern approaches. The material is complemented with historical remarks on the Schwarz Lemma and a chapter introducing some challenging open problems.

The book will be of interest for researchers and postgraduate students in function theory and hyperbolic geometry.

Reviews

From the reviews:

“The aim of this book is to give a unified presentation of some recent results in geometric function theory together with a consideration of their historical sources. The extensive historical references are … interesting, thorough and informative. … this book is filled with many challenging conjectures and suggested problems for exploring new research. In summary this is a delightful book that anyone interested in interrelating geometry and classical geometric function theory should read.”­­­ (Roger W. Barnard, Mathematical Reviews, Issue 2010 j)

Table of contents (8 chapters)

Table of contents (8 chapters)

Buy this book

eBook $54.99
price for USA in USD
  • ISBN 978-3-0346-0000-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $69.99
price for USA in USD
  • ISBN 978-3-7643-9999-3
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Schwarz-Pick Type Inequalities
Authors
Series Title
Frontiers in Mathematics
Copyright
2009
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Basel
eBook ISBN
978-3-0346-0000-2
DOI
10.1007/978-3-0346-0000-2
Softcover ISBN
978-3-7643-9999-3
Series ISSN
1660-8046
Edition Number
1
Number of Pages
VIII, 156
Topics

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