Last edited by JoJozshura

Sunday, August 2, 2020 | History

2 edition of **Conformal Mappings and Teichmüller spaces.** found in the catalog.

Conformal Mappings and Teichmüller spaces.

Olli Lehto

- 204 Want to read
- 11 Currently reading

Published
**1973**
by Israel Institute of Technology in Haifa, Israel
.

Written in

- Conformal mapping.,
- Teichmüller spaces.

**Edition Notes**

Contributions | Ṭekhniyon, Makhon ṭekhnologi le-Yiśraʾel. |

The Physical Object | |
---|---|

Pagination | 58 |

Number of Pages | 58 |

ID Numbers | |

Open Library | OL21949912M |

Many graduate students and other mathematicians have learned the foundations of the theories of quasiconformal mappings and Teichmuller spaces from these lecture notes. This edition includes three new first, written by Earle and Kra, describes further developments in the theory of Teichmuller spaces and provides many references to. Classes of (locally) biholomorphic and (locally) conformal maps in C coincide. Therefore, each complex curve corresponds to a conformal structure on the 2-dimensional surface S(maximal atlas with conformal transition maps). Riemann surface with punctures X is obtained from a Riemann surface X¯ by removing some discrete set of points.

Here I am to just introducing some nice books that are both in my research interests and general interests in mathematics. You may find them useful for your own study/research. I have tried my best to only mentioned books that I have either studied them (fully/partially) or . Mg of distinct conformal structures has complex dimension 3g −3. The space Mg is called the Riemann’s moduli space. The algebraic geometers have studied this space extensively. During the late s, Teichm¨uller followed an analytic approach, using quasiconformal mappings, and constructed a new space Tg, now called the Teichm¨uller Size: KB.

In , H. Weyl defined a Riemann surface as a complex manifold of dimension one. Moreover, Teichmüller's theory of quasiconformal mappings and Teichmüller spaces made a start for new development of the theory of moduli, making possible a complex analytic approach toward the theory of moduli of Riemann surfaces. 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.

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The monograph is concerned with the modulus of families of curves on Riemann surfaces and its applications to extremal problems for conformal, quasiconformal mappings, and the extension of the modulus onto Teichmüller spaces.

The monograph is concerned with the modulus of families of curves on Riemann surfaces and its applications to extremal problems for conformal, quasiconformal mappings, and the extension of the modulus onto Teichmüller spaces.

The main part of the monograph deals Brand: Springer-Verlag Berlin Heidelberg. The Teichmüller spaces (,) and (,) are naturally realised as the upper half-plane, as can be seen using Fenchel–Nielsen coordinates. Teichmüller space and conformal structures [ edit ] Instead of complex structures of hyperbolic metrics one can define Teichmüller space using conformal structures.

Univalent functions and Teichmüller spaces. Conformal Mappings with Quasiconformal Extensions.- Deviation from Mobius transformations.- Dependence of a mapping on its complex dilatation.- Schwarzian derivatives and complex dilatations.- Asymptotic estimates.- Majorant principle.- Coefficient estimates.

Buy Moduli of Families of Curves for Conformal and Quasiconformal Mappings (Lecture Notes in Mathematics) on FREE SHIPPING on qualified ordersCited by: The Teichmüller space \(T(X)\) is the space of marked conformal structures on a given quasiconformal surface \(X\).

This volume uses quasiconformal mapping to give a unified and up-to-date treatment of \(T(X)\). Emphasis is placed on parts of the theory applicable to noncompact surfaces and to surfaces possibly of infinite analytic type.

The theory of Teichmüller spaces studies the different conformal structures on a Riemann surface. After Conformal Mappings and Teichmüller spaces.

book introduction of quasiconformal mappings into the subject, the theory can be said to deal with classes consisting of quasiconformal mappings of a Riemann surface. The first, written by Earle and Kra, describes further developments in the theory of Teichmüller spaces and provides many references to the vast literature on Teichmüller spaces and quasiconformal mappings.

The second, by Shishikura, describes how quasiconformal mappings have revitalized the subject of complex dynamics. quasiconformal mappings and their applications quasiconformal mappings, and the extension of the modulus onto Teichmüller spaces.

The main part of the monograph deals with extremal problems for compact classes of univalent conformal and quasiconformal mappings. Beginning with the classical Riemann mapping theorem, there is a lot of. This chapter presents the solutions of the problems for the Teichmüller spaces T (g, n) and answers a question of Bers by showing that the Bers fiber space F (T) for a group with elliptic elements is usually not (isomorphic to) a Teichmüller space.

The chapter presents the biholomorphic self-mappings of T (g, n). Univalent Functions and Teichmüller Spaces Olli Lehto (auth.) Categories: Mathematics. Year: Edition: 1. Publisher: mappings follows complex plane surface conformal riemann function points proof You can write a book review and share your experiences.

Other readers will always be. This volume contains the proceedings of the AMS Special Session on Quasiconformal Mappings, Riemann Surfaces, and Teichmüller Spaces, held in honor of Clifford J.

Earle, from October 2–3,in Syracuse, New York. This volume includes a wide range of papers on Teichmüller theory and related areas. The Teichmüller space Tg of genus g will be constructed as the set of marked closed Riemann surfaces of genus g.

We also study the space from the viewpoint of quasiconformal mappings and. Lars Ahlfors's Lectures on Quasiconformal Mappings, based on a course he gave at Harvard University in the spring term ofwas first published in and was soon recognized as the classic it was shortly destined to become.

These lectures develop the theory of quasiconformal mappings from scratch, give a self-contained treatment of the Beltrami equation, and cover the basic properties of.

Recently, these spaces are generalized by Yanagishita [10] taking the action of a Fuchsian group Γ into consideration and integrable Teichmüller spaces of Riemann surfaces D /Γ are introduced. Author: Hui Guo. cations of conformal mappings. The ﬁnal section contains a brief introduction to complex integration and a few of its applications.

Further developments and additional details and results can be found in a wide variety of texts devoted to complex analysis, including [1,11,20,21]. Complex Functions. A nonexistence result on harmonic diffeomorphisms between punctured spaces Du, Shi-Zhong and Fan, Xu-Qian, Differential and Integral Equations, Conformal invariants defined by harmonic functions on Riemann surfaces SHIGA, Hiroshige, Journal of Cited by: From inﬁnite-dimensional Teichmüller theory to conformal ﬁeld theory and back.

2/ Table of contents 1 Introduction Overview Conformal Field Theory 2 Teichmüller Theory Quasiconformal Maps Riemann surfaces Deﬁnition and Facts 3 Sewing 4 Fiber Structure of Teichmüller space Fiber Model 5 Schiffer variation rigged moduli spaces. Samuel L. Krushkal, in Handbook of Complex Analysis, Teichmüller’s theory of extremal quasiconformal maps.

In Teichmüller gave an extremely fruitful extension of the Grötzsch problem to the maps of Riemann surfaces of finite analytic type. Recall that a Riemann surface X is a connected one-dimensional complex manifold, i.e., a topological surface endowed with a conformal.

Thanks for contributing an answer to Mathematics Stack Exchange. Please be sure to answer the question. Provide details and share your research. But avoid Asking for help, clarification, or responding to other answers. Making statements based on opinion; back them up with references or personal experience.

Use MathJax to format equations. action on spaces of quadratic di erentials, Veech groups and Veech surfaces. These fall outside the scope of this article.

We refer to the article of Hubert, Lanneau and Moeller in these proceedings for a discussion of these last subjects. For general references for Teichmuller theory, and quasi-conformal mappings I refer toFile Size: KB.In the Teichmüller theory of Riemann surfaces, besides the classical theory of quasi-conformal mappings, vari- ous approaches from differential geometry and algebraic geometry have merged in recent years.

Thus the central subject of "Complex Structure" was a timely choice for .This book is the first comprehensive account of the theory of planar harmonic mappings, treating both the generalizations of univalent analytic functions and the connections with minimal surfaces.

Essentially self-contained, the book contains background material in complex analysis and a full development of the classical theory of minimal.