Univalent Functions And Teichm Ller Spaces

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Univalent Functions And Teichmuller Spaces

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Author : O. Lehto
language : en
Publisher:
Release Date : 1986-12-01

Univalent Functions And Teichmuller Spaces written by O. Lehto and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986-12-01 with categories.

Univalent Functions And Teichm Uller Spaces

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Author : Olli Lehto
language : en
Publisher:
Release Date : 1987

Univalent Functions And Teichm Uller Spaces written by Olli Lehto and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Univalent functions categories.

Univalent Functions And Teichm Ller Spaces

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Author : O. Lehto
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Univalent Functions And Teichm Ller Spaces written by O. Lehto and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

This monograph grew out of the notes relating to the lecture courses that I gave at the University of Helsinki from 1977 to 1979, at the Eidgenossische Technische Hochschule Zurich in 1980, and at the University of Minnesota in 1982. The book presumably would never have been written without Fred Gehring's continuous encouragement. Thanks to the arrangements made by Edgar Reich and David Storvick, I was able to spend the fall term of 1982 in Minneapolis and do a good part of the writing there. Back in Finland, other commitments delayed the completion of the text. At the final stages of preparing the manuscript, I was assisted first by Mika Seppala and then by Jouni Luukkainen, who both had a grant from the Academy of Finland. I am greatly indebted to them for the improvements they made in the text. I also received valuable advice and criticism from Kari Astala, Richard Fehlmann, Barbara Flinn, Fred Gehring, Pentti Jarvi, Irwin Kra, Matti Lehtinen, I1ppo Louhivaara, Bruce Palka, Kurt Strebel, Kalevi Suominen, Pekka Tukia and Kalle Virtanen. To all of them I would like to express my gratitude. Raili Pauninsalo deserves special thanks for her patience and great care in typing the manuscript. Finally, I thank the editors for accepting my text in Springer-Verlag's well known series. Helsinki, Finland June 1986 Olli Lehto Contents Preface. ... v Introduction ...

Weil Petersson Metric On The Universal Teichmuller Space

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Author : Leon Armenovich Takhtadzhi︠a︡n
language : en
Publisher: American Mathematical Soc.
Release Date : 2006

Weil Petersson Metric On The Universal Teichmuller Space written by Leon Armenovich Takhtadzhi︠a︡n and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.

In this memoir, we prove that the universal Teichmuller space $T(1)$ carries a new structure of a complex Hilbert manifold and show that the connected component of the identity of $T(1)$ -- the Hilbert submanifold $T {0 (1)$ -- is a topological group. We define a Weil-Petersson metric on $T(1)$ by Hilbert space inner products on tangent spaces, compute its Riemann curvature tensor, and show that $T(1)$ is a Kahler-Einstein manifold with negative Ricci and sectional curvatures. We introduce and compute Mumford-Miller-Morita characteristic forms for the vertical tangent bundle of the universal Teichmuller curve fibration over the universal Teichmuller space. As an application, we derive Wolpert curvature formulas for the finite-dimensional Teichmuller spaces from the formulas for the universal Teichmuller space. We study in detail the Hilbert manifold structure on $T {0 (1)$ and characterize points on $T {0 (1)$ in terms of Bers and pre-Bers embeddings by proving that the Grunsky operators $B {1 $ and The results of this memoir were presented in our e-prints: Weil-Petersson metric on the universal Teichmuller space I. Curvature properties and Chern forms, arXiv:math.CV/0312172 (2003), and Weil-Petersson metric on the universal Teichmuller space II. Kahler potential and period mapping, arXiv:math.CV/0406408 (2004).

Univalent Functions

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Author : Derek K. Thomas
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-04-09

Univalent Functions written by Derek K. Thomas and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-09 with Mathematics categories.

The study of univalent functions dates back to the early years of the 20th century, and is one of the most popular research areas in complex analysis. This book is directed at introducing and bringing up to date current research in the area of univalent functions, with an emphasis on the important subclasses, thus providing an accessible resource suitable for both beginning and experienced researchers. Contents Univalent Functions – the Elementary Theory Definitions of Major Subclasses Fundamental Lemmas Starlike and Convex Functions Starlike and Convex Functions of Order α Strongly Starlike and Convex Functions Alpha-Convex Functions Gamma-Starlike Functions Close-to-Convex Functions Bazilevič Functions B1(α) Bazilevič Functions The Class U(λ) Convolutions Meromorphic Univalent Functions Loewner Theory Other Topics Open Problems

New Trends In Geometric Function Theory And Applications Proceedings Of The International Conference

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Author : O P Juneja
language : en
Publisher: #N/A
Release Date : 1991-05-17

New Trends In Geometric Function Theory And Applications Proceedings Of The International Conference written by O P Juneja and has been published by #N/A this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-05-17 with categories.

After the positive settlement of Bieberbach's conjecture by Prof. Louis dé Branges, there are new avenues open for researchers in the field of Geometric Function Theory. New directions of research and new problems arising in this field are mainly considered in this proceedings.

Handbook Of Complex Analysis

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Author : Reiner Kuhnau
language : en
Publisher: Elsevier
Release Date : 2002-12-05

Handbook Of Complex Analysis written by Reiner Kuhnau and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-12-05 with Mathematics categories.

Geometric Function Theory is a central part of Complex Analysis (one complex variable). The Handbook of Complex Analysis - Geometric Function Theory deals with this field and its many ramifications and relations to other areas of mathematics and physics. The theory of conformal and quasiconformal mappings plays a central role in this Handbook, for example a priori-estimates for these mappings which arise from solving extremal problems, and constructive methods are considered. As a new field the theory of circle packings which goes back to P. Koebe is included. The Handbook should be useful for experts as well as for mathematicians working in other areas, as well as for physicists and engineers. · A collection of independent survey articles in the field of GeometricFunction Theory · Existence theorems and qualitative properties of conformal and quasiconformal mappings · A bibliography, including many hints to applications in electrostatics, heat conduction, potential flows (in the plane)

Analytic Functions

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Author : Lars Valerian Ahlfors
language : en
Publisher: Princeton University Press
Release Date : 2015-12-08

Analytic Functions written by Lars Valerian Ahlfors and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-08 with Mathematics categories.

A survey of recent developments both in the classical and modern fields of the theory. Contents include: The complex analytic structure of the space of closed Riemann surfaces; Complex analysis on noncompact Riemann domains; Proof of the Teichmuller-Ahlfors theorem; The conformal mapping of Riemann surfaces; On certain coefficients of univalent functions; Compact analytic surfaces; On differentiable mappings; Deformations of complex analytic manifolds. Originally published in 1960. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Univalent Functions Selected Topics

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Author : G. Schober
language : en
Publisher: Springer
Release Date : 2006-11-14

Univalent Functions Selected Topics written by G. Schober and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.

Handbook Of Complex Analysis

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Author : Reiner Kuhnau
language : en
Publisher: Elsevier
Release Date : 2004-12-09

Handbook Of Complex Analysis written by Reiner Kuhnau and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-12-09 with Mathematics categories.

Geometric Function Theory is that part of Complex Analysis which covers the theory of conformal and quasiconformal mappings. Beginning with the classical Riemann mapping theorem, there is a lot of existence theorems for canonical conformal mappings. On the other side there is an extensive theory of qualitative properties of conformal and quasiconformal mappings, concerning mainly a prior estimates, so called distortion theorems (including the Bieberbach conjecture with the proof of the Branges). Here a starting point was the classical Scharz lemma, and then Koebe's distortion theorem. There are several connections to mathematical physics, because of the relations to potential theory (in the plane). The Handbook of Geometric Function Theory contains also an article about constructive methods and further a Bibliography including applications eg: to electroxtatic problems, heat conduction, potential flows (in the plane). · A collection of independent survey articles in the field of GeometricFunction Theory · Existence theorems and qualitative properties of conformal and quasiconformal mappings · A bibliography, including many hints to applications in electrostatics, heat conduction, potential flows (in the plane).