Download Quasiconformal Teichmuller theory by Frederick P. Gardiner PDF

By Frederick P. Gardiner

The Teichmuller house $T(X)$ is the gap of marked conformal constructions on a given quasiconformal floor $X$. This quantity makes use of quasiconformal mapping to offer a unified and updated remedy of $T(X)$. Emphasis is put on components of the speculation appropriate to noncompact surfaces and to surfaces in all probability of limitless analytic sort. The publication offers a remedy of deformations of advanced constructions on endless Riemann surfaces and offers heritage for extra learn in lots of components. those comprise functions to fractal geometry, to 3-dimensional manifolds via its dating to Kleinian teams, and to one-dimensional dynamics via its dating to quasisymmetric mappings. Many study difficulties within the software of functionality thought to geometry and dynamics are urged

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Extra info for Quasiconformal Teichmuller theory

Example text

En X~(Tn)), pour On lemme M = nage V ~) un = Ilm il e x l s t e zl fonction ~ hk = 4-k darts le cas p&riodique assez grand [2] on p e u t w 7 de dgmonstration lemme darts le du t h @ o r ~ m e W ~ variable supposer I w 6 de . induit reste locale p on par un X g~n est fondamental. un valable en C exercice sim- en classe C espaces de c l a s s e en C r ). (et ~ C ale V ~ (resp. il e x i s t e lemme s@par@es. ,fn) Y I le lemme ~= se d o n n e V M de ; alors V ~) de Y dans C r voisinage, et qgDiff~(T tel n) X m ( T n) que (resp.

Salt que On pose des Y et y" -- p~l o~ les yT I sont boules d'apr~s y-I des diff,- le lemme 2. P8 Yi que = Comme y,-1 = ~ support N et On y ~ Ker Y' 8 = JS(Y) N Pu parfaits. de l ' i d e n t i t ~ . En g g n ~ r a l symplectiques -I Pu Y' { smnt : u = a + 6 avec On volt Ker a Pu gj ~ P8 ~gal s'~crit alors sur (p-I Yi P6 )" rOtations --1 ~boule Bj et supp yj u P8 (supp y~) C Boule U~ . B'. et U'. demx b o u l e s J J le c o r o l l a i r e , il existe des fj ggal N H i=I telles que B. C B'. et U.

T . h t DES classique une base (voir finie jours choisir les qu'il en est ainsi. des [3], page stable. (iii)' : si ft (iii)' , 0 $ t t reste families ht(0) , oG ~ I, darts un v o i - de d i f f @ o m o r p h i s - m U pour tout t. EQUIVARIANTES. ,Pk(x P. h o m o g ~ n e s ~ tout des , avec APPLICATIONS ~ 1 , . . , X n ]G" l ' a l g ~ b r e un r @ s u l t a t (i) de que Les stable. 3 que de f, = 0. stable. @quivariante de t et H t t e l l e s Q,U E L Q U E S @quivariante homotopique petit telle : diff@rentiable suffisamment il e x i s t e gquivariante @quivalentes (i) est une Soit sont (ii) d@signe sinage application suivantes On m o n t r e r a 2.

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