Pdf quasiconformal maps and teichmuller theoryextremal. The latter brought the theory of quasiconformal mappings to a high level of development. Tight contact structures on fibred honda, ko, kazez, william h. The classification of homeomorphisms of surfaces 2. Quasiconformal mappings and teichmuller s theorem scholars choice edition. Geometry of teichmuller space with the teichmuller metric howard masur january 20, 2010 1 introduction the purpose of this chapter is to describe recent progress in the study of teichmuller geometry. I read a little bit on kashaevs or chekhov and focks, but find that i need to fill. Review of teichmuller theory and applications to geometry. Volumes 2 through 4 prove four theorems by william thurston. Newest teichmullertheory questions feed subscribe to rss. Towards a modular functor from quantum higher teichmuller theory gus schrader university of california, berkeley berkeley tokyo workshop on quantum field theory and subfactors november 18, 2016 gus schrader uc berkeley quantum higher teichmuller theory berkeley tokyo workshop on quantum field theory and subfactors november 18, 2016 1 19.
There is also a version of teichmuller contraction for atr. Quasiconformal mapping encyclopedia of mathematics. The universal teichmuller space t, introduced by ahlfors and bers, plays a key role in the theory of quasiconformal maps and riemann surfaces. Each appendix is a brief survey of a theory used in the book and the glossary gives explanations of terms that are not. A quasiconformal map is the uniquely extremal representative in its teichmuller class if and only if its beltrami coefficient \i is uniquely ex tremal in its infinitesimal class.
The book is aimed at readers who have completed at least a year of graduate school, in conformity with the advanced level of the material. A survey of the very important weilpetersson metric can be found in w. There are more than 1 million books that have been enjoyed by people from all over the world. There is a unique quasiconformal map from x1 to x2 realizing this distance. Harvard university, cambridge ma 028 cuny grad center, new york, ny and suny, stony brook, ny 20 november, 1993 contents. Teichmuller theory and applications to geometry, topology, and dynamics volume 1. By means of quasiconformal mapping theory, we prove that the bers projection and preprojection. In material representation, the evolution is governed. By equivariance, h descends to a homotopy hfrom to axis h i. Tang shuan school of mathematics sciences, guizhou normal university, guiyang 550001, china abstract. Quasiconformal mappings, riemann surfaces, and teichmuller spaces. Amazon advertising find, attract, and engage customers. The fenchelnielsen coordinates so named after werner fenchel and jakob nielsen on the teichmuller space are associated to a pants decomposition of the surface.
Much of the theory of riemann surfaces boils down to the following theorem. He used it in an essential way in his investigations of. The first volume gave an introduction to teichmuller theory. Always update books hourly, if not looking, search in the book search column. Quasiconformal mappings and teichmullers theorem scholars. The first, written by earle and kra, describes further developments in the theory of teichmuller spaces and provides many references to the vast literature on teichmuller spaces and quasiconformal mappings. This volume includes a wide range of papers on teichmuller theory and related areas. Comments new 20180403 3 an introduction to padic teichmuller theory. An introduction to the theory of higherdimensional quasiconformal mappings american mathematical society gehring, frederick w.
It is well known since the work ofarnold1966 that the solutions of the euler equations are the spatial representation of the geodesics on the group of volume preserving di eomorphisms. Quasiconformal mappings, from ptolemys geography to the work of. Quasiconformal mappings and their applications download. Complex structures, jacobians and the weil petersson form 31 lecture 4. Pdf padic teichmuller theory 1 a theory of ordinary padic curves. The second, by shishikura, describes how quasiconformal mappings have revitalized the subject of complex dynamics. Teichmuller space encodes the possible number of ways in which you can deform complex structure on a space. This volume contains the proceedings of the ams special session on quasiconformal mappings, riemann surfaces, and teichmuller spaces, held in honor of clifford j.
Teichmuller theory is one of those few wonderful subjects which bring together, at an equally important. This site is like a library, use search box in the widget to get ebook that you want. The second of four volumes devoted to teichmuller theory and its applications to geometry, topology, and dynamics, this volume proves two theorems by william thurston. I would like to ask for some detailed reference for quantum teichmuller theory, better in a mathematical taste. Quasiconformal mappings and teichmuller s theorem scholars choice edition bers, lipman on. Handbook of teichm ller theory ebook download free pdf. This set of notes contains basic material on riemann surfaces, teichmu. Preface xvn this result is called teichmuller contraction. The geometry of the universal teichmuller space and the. The importance of quasiconformal mappings in complex analysis was realized by ahlfors and teich muller in the 1930s. He introduced quasiconformal mappings and differential geometric methods into the study of riemann surfaces. Teichmuller theory the teichmuller space of a riemann surface is the space of all deformations of the complex structure, with a topological marking that insures that the teichmuller space is simply connected. Emphasis is placed on parts of the theory applicable to noncompact surfaces and to surfaces possibly of infinite analytic type.
Introduction the roots of quasiconformal theory lie in geography, more precisely in the study of mappings from subsets of the sphere to the euclidean plane, and the attempts to nd the \best such mappings. The first, written by earle and kra, describes further developments in the theory of teichmuller spaces quwsiconformal provides many references to the vast literature on teichmuller spaces and quasiconformal mappings. The author ends his book with a consideration of teichmuller spaces, with attention given to the extent to which the classical theory of conformally equivalent riemann surfaces can be generalized to the context of quasiconformal mappings. Ahlfors used quasiconformal mappings in his geometric approach to nevanlinnas value distribution theory. This volume uses quasiconformal mapping to give a unified and uptodate treatment of \tx\. Earle, from october 23, 2010, in syracuse, new york. In the same way that a quasiconformal mapping turns out to be a mobius transformation even without the a priori assumption that it is a homeomorphism, a quasiconformal mapping is locally homeomorphic as soon as its coefficient of quasiconformality is sufficiently close to 1. Based on a series of graduate lectures given by vladimir markovic at the university of warwick in spring 2003, this book is accessible to those with a grounding in complex analysis looking for an introduction to the theory of quasiconformal maps and teichmuller theory. These lectures develop the theory of quasiconformal mappings from scratch, give a selfcontained treatment of the beltrami equation, and cover the basic. Gardiner and jun hu proceedings of the year on teichmuller theory hri, allahabad, volume 10, 2009, pages 195228 abstract we present a brief exposition of teichmullers theorem. Click download or read online button to get quasiconformal mappings and their applications book now.
Teichmuller space, which give a very nice description of the space for certain. Teichmuller theory and applications matrix editions. Stroock, an introduction to the analysis of paths on a riemannian manifold, 2000 73 john locker, spectral theory of nonselfadjoint twopoint differential operators, 2000. Introduction an orientation preserving homeomorphism f from a riemann surface x onto a riemann surface y is given.
The authors have produced a formidable treatise on the modern theories of quasiconformal mappings, riemann surfaces and teichmuller. The moduli space mg of the riemann surfaces of genus g is the quotient space of the teichmuller. Then the homotopy from to lifts to a homotopy and a geodesic lift g of. Quasiconformal mappings and teichmuller s theorem by bers, lipman. Today, teichmuller theory is a substantial area of mathematics that has inter. An introduction to the theory of higher dimensional. Lars ahlforss lectures on quasiconformal mappings, based on a course he gave at harvard university in the spring term of 1964, was first published in 1966 and was soon recognized as the classic it was shortly destined to become. The functorial mathematical definition of conformal field theory was first formulated approximately 30 years ago. What is a good introduction to teichmuller theory, mapping class groups etc. Abstract we present a brief exposition of teichmullers. As a service to our customers we are providing this early version of the manuscript. Quasiconformal maps and teichmuller theory alastair. Request pdf quasiconformal mappings, from ptolemys geography to the work of teichm\\uller the origin of quasiconformal mappings, like that of conformal mappings, can be traced back to old.
Each point in may be regarded as an isomorphism class of marked riemann surfaces, where a marking is an isotopy class of homeomorphisms from to itself. Harmonic measure and polynomial julia sets binder, i. Introduction an orientation preserving homeomorphism ffrom a riemann surface x onto a riemann surface y is given. Quasiconformal mappings, from ptolemys geography to the work. Gardiner and jun hu winter, 2005, hri, allahabad, india. Inspired by the research work of sharon and mumford on 2d shape analysis recently it has been generalized to model multiple 2d contours, we build a teichmuller space for 3d shapes by using conformal mappings. Teichmuller theory mathematisches institut uni bonn. Interuniversal teichmuller theory i construction of hodge theaters shinichi mochizuki april2020 abstract. Teichmullers work on quasiconformal mappings 43 references 55 1. He also coined the term quasiconformalinhis1935workonuberlagerungs. This section gives a summary of the basics of teichmull.
Quasiconformal mappings, riemann surfaces, and teichmuller. The teichmuller space is thus defined as the collection of pairs of riemann surfaces and sensepreserving. For a 3d surface, all the contours represent the shape of the surface. In section 4 we have a closer look at teichmuller space. It is based on a course i taught at university of utah in 19921993. Click download or read online button to get an introduction to the theory of higher dimensional quasiconformal mappings book.
Geometry of teichmuller space with the teichmuller metric. Athanase papadopoulos teichmuller theory is one of those few wonderful subjects which bring together, at an equally important level, fundamental ideas coming from different. Stability for infinitedimensional fibre bundles sakai, katsuro, tsukuba journal of mathematics, 1981. Brain morphometry on congenital hand deformities based on.
This is a pdf file of an unedited manuscript that has been accepted for publication. Gardiner and nikola lakic, quasiconformal teichmuller theory, 2000 75 greg hjorth, classification and orbit equivalence relations, 2000 74 daniel w. Quasiconformal teichmuller theory as an analytical foundation for. Quasiconformal mappings and teichmullers theorem by bers, lipman. Pdf comments new 20110715 2 foundations of padic teichmuller theory.
This volume is the second of four volumes devoted to teichmuller theory and its applications to geometry, topology, and dynamics. Righthand side only of paper has text, and page numbers there is no table of contents. Results from riemann surface theory and quasiconformal. The discussion on quasiconformal mappings in chapter 4 is very important but might be one of the most difficult parts of this volume. Other readers will always be interested in your opinion of the books youve read. Regarding teichmullers work, ahlfors, in his 1953 paper on the development of the theory of conformal mapping and riemann surfaces through. This paper study the bers projection and preprojection of qkteichmuller.
Introduction much of the theory of riemann surfaces boils down to the following theorem, the twodimensional equivalent of thurstons. The teichmuller space \tx\ is the space of marked conformal structures on a given quasiconformal surface \x\. After the 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 book provides a treatment of deformations of complex structures on infinite riemann surfaces and gives background for further research in many areas. Jul 14, 2006 the author ends his book with a consideration of teichmuller spaces, with attention given to the extent to which the classical theory of conformally equivalent riemann surfaces can be generalized to the context of quasiconformal mappings. Quasiconformal maps and teichmuller theoryextremal mappings, overview article pdf available in bulletin classe des sciences mathematiques et natturalles 14538 january 20 with 410 reads. Lectures on quasiconformal mappings university lecture. A quasiconformal mapping class is a homotopy equivalence class. By the theory of quasiconformal mappings, any complex structure on a sur. This is a decomposition of into pairs of pants, and to each curve in the decomposition is associated its length in the hyperbolic metric corresponding to the point in teichmuller space, and another real parameter called the. Whether youve loved the book or not, if you give your honest and detailed thoughts then people will find new books that are right for them. Quasiconformal homeomorphisms and dynamics iii harvard. This course was a prequel to the 19931994 course on thurston s hyperbolization theorem which later became a book k.