By Yoichi Imayoshi, Masahiko Taniguchi

This e-book bargains a simple and compact entry to the idea of Teichm?ller areas, ranging from the main basic facets to the latest advancements, e.g. the position this thought performs in regards to thread idea. Teichm?ller areas supply parametrization of all of the complicated buildings on a given Riemann floor. This topic is said to many alternative components of arithmetic together with advanced research, algebraic geometry, differential geometry, topology in and 3 dimensions, Kleinian and Fuchsian teams, automorphic types, complicated dynamics, and ergodic idea. lately, Teichm?ller areas have began to play a massive position in string concept. Imayoshi and Taniguchi have tried to make the ebook as self-contained as attainable. They current a number of examples and heuristic arguments for you to support the reader seize the information of Teichm?ller conception. The publication could be a very good resource of knowledge for graduate scholars and reserachers in complicated research and algebraic geometry in addition to for theoretical physicists operating in quantum idea.

**Read or Download An introduction to Teichmüller spaces PDF**

**Similar differential geometry books**

**Metric Foliations and Curvature**

Some time past 3 or 4 a long time, there was expanding consciousness that metric foliations play a key position in realizing the constitution of Riemannian manifolds, relatively people with confident or nonnegative sectional curvature. in reality, all identified such areas are made out of just a consultant handful via metric fibrations or deformations thereof.

**Proceedings of the international congress of mathematicians. Beijing 2002**

The Fields Medal - arithmetic' identical of the Nobel Prize - is gifted in the course of the foreign Congress of Mathematicians (ICM) to acknowledge impressive mathematical fulfillment. whilst, the foreign Mathematical Union awards the Nevanlinna Prize for paintings within the box of theoretical machine technology.

**Differentialgeometrie und homogene Räume**

Das Ziel dieses Buches ist, im Umfang einer zweisemestrigen Vorlesung die wichtigsten Grundlagen der Riemannschen Geometrie mit allen notwendigen Zwischenresultaten bereitzustellen und die zentrale Beispielklasse der homogenen Räume ausführlich darzustellen. Homogene Räume sind Riemannsche Mannigfaltigkeiten, deren Isometriegruppe transitiv auf ihnen operiert.

- Differential geometry and topology
- Notes on Geometry
- An Invitation to Web Geometry
- Compact Riemann Surfaces: An Introduction to Contemporary Mathematics
- Differential Harnack inequalities and the Ricci flow

**Additional info for An introduction to Teichmüller spaces**

**Example text**

O 2 p o o t l . r o q q \ n u a l q l p n s o f l e r e q l ' U ) g f . r a a a i o g ( n ) (i) For any P, if E R with 7I"(p) = 71" (if) , there exists an element I E r with if = I(P)· (ii) For every pER, there is a suitable neighborhood U of p in R such that I( U) n U = ¢ for every I E r - {id}. In particular, each element of r except for the identity has no fixed points. (iii) r acts properly discontinuously on R; that is,for any compact subset K of R, there are at most finitely many elements I E r such that I(K) n K f.

Sup11l*+ IIIlI(z)1 Kr . 00. lrrl'J! ()I zED z) l , e b r -- l pIII coefficient Ill. W" call K I d,ilatationof ff.. call K1 the maximal dilatation quasiconformal mappings. mappings. We We shall shall In this chapter, we only consider consider smooth quasiconformal chapter, we quasiconformal mappings 4. study more general general quasiconformal mappings in Chapter 4. 4) lprl(z)l of the = diffeomorpJQ)dzldz an orientation-preserving Beltrami = III (z) di/ dz of an orientation-preserving diffeomorcoefficient III Beltrami coefficient W is aa - S l?.

0}. 4. 6, that is, every element element of r f except except for the unit is, unit element element has has no fixed points in R, E, and acts properly disconti~uously discontinuously on R. acts E. f e E fr satisfying 4=t@). ii = I(P), Denote Denote by [p] equivalence class the equivalence class [f] of the set of of fi. p. he of all these these equivalence equivalence classes cl~ses [PJ, called the p], which is called quolient quotient space space of of r? i-. r. Define Define the projection 7r: RI r by r(fi) 7r(p) == [p].