This site is like a library, use search box in the widget to get ebook that you want. 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 teichmuller s theorem. Quasiconformal homeomorphisms and dynamics iii harvard. Jan 10, 2015 the mantra is studying objects in families gives important information about the individual objects. Assuming some prior familiarity with riemann surfaces and hyperbolic geometry, the text is illustrated throughout by examples and exercises. Know that ebook versions of most of our titles are still available and may be downloaded. 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. Quasiconformal maps and teichmuller theory book, 2007. Let ljt be the unique geodesic in the free homotopy class of the closed. Use 3 disjoint mutually nonseparating geodesics in h2 such that hyperbolic distances between them are the numbers.
Online pdf quasiconformal maps and teichmuller theory. Gardiner and nikola lakic, quasiconformal teichmuller theory, 2000 75 greg hjorth, classification and orbit equivalence relations, 2000 74 daniel w. Introduction to teichmuller theory, old and new ems publishing. Teichmuller theory, for general surfaces, there is an one to one correspondence between the set of quasi. Introduction an orientation preserving homeomorphism ffrom a riemann surface x onto a riemann surface y is given. Holomorphic motions and quasiconformal conjugacies. In the case of a surface with one puncture, the fundamental group is a free. Interuniversal teichmuller theory i construction of hodge theaters shinichi mochizuki april2020 abstract. Abstract we present a brief exposition of teichmuller s. Teichmuller s work on quasiconformal mappings 43 references 55 1.
Teichmuller theory is one of those few wonderful subjects which bring together, at an equally important. Teichmuller space encodes the possible number of ways in which you can deform complex structure on a space. Stroock, an introduction to the analysis of paths on a riemannian manifold, 2000 73 john locker, spectral theory of nonselfadjoint twopoint differential operators, 2000. Therefore the mapping class group acts on free homotopy classes of. Teichmullers work on quasiconformal mappings 43 references 55 1. Quasiconformal teichmuller theory as an analytical foundation for twodimensional conformal field theory chapter pdf available january 2017 with 40 reads how we measure reads. This volume uses quasiconformal mapping to give a unified and uptodate treatment of \tx\. Quasiconformal mappings, from ptolemys geography to the work of. Quasiconformal maps and teichmuller theoryextremal mappings, overview article pdf available in bulletin classe des sciences mathematiques et natturalles 14538 january 20 with 439 reads.
Complex structures, jacobians and the weil petersson form 31 lecture 4. The patterson and bersgreenberg isomorphism theorems 29 2. Hubbard teichmuller theory pdf vector calculus, linear algebra, and differential forms, a unified approach with barbara burke hubbard. If youre more analytically minded, i recommend gardiner and lakic, quasiconformal teichmuller theory thoery nag, the complex analytic theory of teichmuller spaces. Preprint 1 computing quasiconformal maps on riemann surfaces.
Aimed at graduates with a grounding in complex analysis, this book provides an accessible introduction to the theory of quasiconformal maps and teichmuller theory. Quasiconformal maps and teichmuller theoryextremal mappings, overview. Quasiconformal mappings, riemann surfaces, and teichmuller spaces. In other words, every quasi conformal map can be fully determined by the beltrami differentials and is unique up to a. A survey of the very important weilpetersson metric can be found in w. 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. A panoramic overview of interuniversal teichmuller theory. What is a good introduction to teichmuller theory, mapping class groups etc. Athanase papadopoulos teichmuller theory is one of those few wonderful subjects which bring together, at an equally important level, fundamental ideas coming from different.
Bers embedding and the bers boundary of teichmuller. Given a quasiconformal hyperbolic surface of nite type, s, the teichmull er space modeled on s, denoted t s, is the set of equivalence classes of pairs x. Xis a quasiconformal homeomorphism, with two such pairs deemed to be equivalent if. Emphasis is placed on parts of the theory applicable to noncompact surfaces and to surfaces possibly of infinite analytic type. 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. An introduction to teichmuller theory notes from a course given by dick canary, fall 2015 november 23, 2015 1 an overview of hyperbolic geometry 1. Extremal quasiconformal mappings with free boundary. Antonakoudis this is an introduction to the theory of conformal dynamical systems, riemann surfaces and their moduli spaces.
Of central importance in the theory of quasiconformal mappings in two dimensions is the measurable riemann mapping theorem, proved by lars ahlfors and lipman bers. 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. Teichmuller theory and quadratic differentials pure. The classical parts of the theory include teichmuller s theorem on the existence and uniqueness of an extremal quasiconformal mapping in a given homotopy class of mappings between riemann surfaces, the theorems of bers and ahlfors on the completeness of poincare theta series for general fuchsian groups and the approximation of integrable. Teichmuller theory is one of those few wonderful subjects which bring together. Abstract we present a brief exposition of teichmullers. Quasiconformal teichmuller theory thoery nag, the complex analytic theory of teichmuller spaces. Riemann surfaces and teichmuller theory l24 stergios m. This volume includes a wide range of papers on teichmuller theory and related areas. Introduction an orientation preserving homeomorphism f from a riemann surface x onto a riemann surface y is given. Quasiconformal mappings and their applications download.
The theorem generalizes the riemann mapping theorem from conformal to quasiconformal homeomorphisms, and is stated as follows. Geometry of teichmuller space with the teichmuller metric. If youre more analytically minded, i recommend gardiner and lakic, quasiconformal teichmuller theory and nag, the complex analytic theory of teichmuller spaces. Univalent functions and teichmuller spaces book, 1987. This volume contains the proceedings of the ams special session on quasiconformal mappings, riemann surfaces, and teichmuller spaces, held in honor of clifford j. Then there exists a complete hyperbolic structure x with geodesic boundary on the pair of pants s2 \ 3 discs such that lengths of boundary curves are l1,l2,l3. Click download or read online button to get quasiconformal mappings and their applications book now. The teichmuller space \tx\ is the space of marked conformal structures on a given quasiconformal surface \x\. Teichmuller theory mathematisches institut universitat bonn. Instead of power series, integral representations, or algebra ic techniques, the theory relies on singular integrals, geometricmeasuretheory,andsobolevspaces. Teichmuller, which are the 20thcentury founders of the theory.
Surface homeomorphisms and rational functions john h. Pdf quasiconformal teichmuller theory as an analytical. The fenchelnielsen coordinates so named after werner fenchel and jakob nielsen on the teichmuller space are associated to a pants decomposition of the surface. Pdf quasiconformal maps and teichmuller theoryextremal. Gardiner and jun hu winter, 2005, hri, allahabad, india. 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. Quasiconformal maps and teichmuller theory alastair. Quasiconformal mappings, from ptolemys geography to the work. Abikoff, w the real analytic theory of teichmuller space.
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