共查询到20条相似文献,搜索用时 0 毫秒
1.
Sudeb Mitra 《Israel Journal of Mathematics》2001,125(1):45-51
We generalize the principle of Teichmüller contraction and deduce the Hamilton-Krushkaĺ condition for extremal quasiconformal
mappings in the Teichmüller space of a closed set in the Riemann sphere. 相似文献
2.
3.
Geometriae Dedicata - We investigate a metric structure on the Thurston boundary of Teichmüller space. To do this, we develop tools in sup metrics and apply Minsky’s... 相似文献
4.
A. G. Sergeev 《Proceedings of the Steklov Institute of Mathematics》2008,263(1):163-188
In the first part of the paper, we describe the Kähler geometry of the universal Teichmüller space, which can be realized as an open subset in the complex Banach space of holomorphic quadratic differentials in the unit disc. The universal Teichmüller space contains classical Teichmüller spaces T(G), where G is a Fuchsian group, as complex submanifolds. The quotient Diff+(S 1)/Möb(S 1) of the diffeomorphism group of the unit circle modulo Möbius transformations can be considered as a “smooth” part of the universal Teichmüller space. In the second part we describe how to quantize Diff+(S 1)/Möb(S 1) by embedding it in an infinite-dimensional Siegel disc. This quantization method does not apply to the whole universal Teichmüller space. However, this space can be quantized using the “quantized calculus” of A. Connes and D. Sullivan. 相似文献
5.
We explicitly describe a noncommutative deformation of the *-algebra of functions on the Teichmüller space of Riemann surfaces
with holes that is equivariant with respect to the action of the mapping class group.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 120, No. 3, pp. 511–528, September, 1999. 相似文献
6.
TANG ShuAn 《中国科学 数学(英文版)》2013,56(3):541-551
In this paper, we prove that the Bers projection of the integrable Teichmller space is holomorphic. By using the Douady-Earle extension, we obtain some characterizations of the integrable Teichmller space as well as the p-integrable asymptotic affine homeomorphism. 相似文献
7.
Hideki Miyachi 《Geometriae Dedicata》2013,162(1):283-304
In this paper, we study the asymptotic behavior of Teichmüller geodesic rays in the Gardiner–Masur compactification. We will observe that any Teichmüller geodesic ray converges in the Gardiner–Masur compactification. Therefore, we get a mapping from the space of projective measured foliations to the Gardiner–Masur boundary by assigning the limits of associated Teichmüller rays. We will show that this mapping is injective but is neither surjective nor continuous. We also discuss the set of points where this mapping is bicontinuous. 相似文献
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Sebastian W. Hensel 《Geometriae Dedicata》2011,155(1):31-67
Let X be a closed hyperbolic surface and λ, η be weighted geodesic multicurves which are short on X. We show that the iterated grafting along λ and η is close in the Teichmüller metric to grafting along a single multicurve which can be given explicitly in terms of λ and
η. Using this result, we study the holonomy lifts gr
λ
ρ
X,λ of Teichmüller geodesics ρ
X,λ for integral laminations λ and show that all of them have bounded Teichmüller distance to the geodesic ρ
X,λ. We obtain analogous results for grafting rays. Finally we consider the asymptotic behaviour of iterated grafting sequences
gr
nλ
X and show that they converge geometrically to a punctured surface. 相似文献
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11.
This paper focuses on Teichmüller curves in the space of two-genus double covers of flat tori,identifying all of them, counting them with respect to their triangular areas, formulating the numbers of their cusps, and characterizing the ones without a simple cusp. Some applications are also discussed. 相似文献
12.
A non-Euclidean crystallographic group F (NEC group, for short) is a discrete subgroup of isometries of the hyperbolic plane H, with compact quotient space H/Г. These groups uniformize Klein surfaces, surfaces endowed with dianalytic structure. These surfaces can be seen as a generalization of Riemann surfaces.
Fundamental polygons play an important role in the study of parametrizations of the Teichmuller space of NEC groups.
In this work we construct a class of right-angled polygons which are fundamental regions of bordered surface NEC groups. The free parameters used in the construction of the polygons give a parametrization of the Teichmuller space. From the parameters we obtain explicit matrices of the generators of the groups. Finally, we give examples to exhibit how different relations between the parameters reflect the existence of automorphisms on the quotient surfaces. 相似文献
Fundamental polygons play an important role in the study of parametrizations of the Teichmuller space of NEC groups.
In this work we construct a class of right-angled polygons which are fundamental regions of bordered surface NEC groups. The free parameters used in the construction of the polygons give a parametrization of the Teichmuller space. From the parameters we obtain explicit matrices of the generators of the groups. Finally, we give examples to exhibit how different relations between the parameters reflect the existence of automorphisms on the quotient surfaces. 相似文献
13.
We show that any element of the universal Teichmüller space is realized by a unique minimal Lagrangian diffeomorphism from
the hyperbolic plane to itself. The proof uses maximal surfaces in the 3-dimensional anti-de Sitter space. We show that, in
AdS
n+1, any subset E of the boundary at infinity which is the boundary at infinity of a space-like hypersurface bounds a maximal space-like hypersurface.
In AdS3, if E is the graph of a quasi-symmetric homeomorphism, then this maximal surface is unique, and it has negative sectional curvature.
As a by-product, we find a simple characterization of quasi-symmetric homeomorphisms of the circle in terms of 3-dimensional
projective geometry. 相似文献
14.
Huiping Pan 《中国科学 数学(英文版)》2023,(8):1751-1766
We show that every R-linear surjective isometry between the cotangent spaces to the Teichmüller space equipped with the Thurston norm is induced by some isometry between the underlying hyperbolic surfaces.This is an analogue of Royden’s theorem concerning the Teichmüller norm. 相似文献
15.
Let X be a non-elementary Riemann surface of type(g,n),where g is the number of genus and n is the number of punctures with 3g-3+n1.Let T(X)be the Teichmller space of X.By constructing a certain subset E of T(X),we show that the convex hull of E with respect to the Teichmller metric,the Carathodory metric and the Weil-Petersson metric is not in any thick part of the Teichmler space,respectively.This implies that convex hulls of thick part of Teichmller space with respect to these metrics are not always in thick part of Teichmller space,as well as the facts that thick part of Teichmller space is not always convex with respect to these metrics. 相似文献
16.
Vladimir Hinich 《Israel Journal of Mathematics》2010,175(1):151-156
We present an example showing that a family of Riemann surfaces obtained by a general plumbing construction does not necessarily give local coordinates on the Teichmüller space. 相似文献
17.
In this paper we explore the idea that Teichmüller space is hyperbolic “on average.” Our approach focuses on studying the geometry of geodesics which spend a definite proportion of time in some thick part of Teichmüller space. We consider several different measures on Teichmüller space and find that this behavior for geodesics is indeed typical. With respect to each of these measures, we show that the average distance between points in a ball of radius r is asymptotic to 2r, which is as large as possible. Our techniques also lead to a statement quantifying the expected thinness of random triangles in Teichmüller space, showing that “most triangles are mostly thin.” 相似文献
18.
We discuss the existence of the angle between two curves in Teichmüller spaces and show that, in any infinite dimensional Teichmüller space, there exist infinitely many geodesic triangles each of which has the same three vertices and satisfies the property that its three sides have the same and arbitrarily given length while its three angles are equal to any given three possibly different numbers from 0 to $\pi $ . This implies that the sum of three angles of a geodesic triangle may be equal to any given number from 0 to $3\pi $ in an infinite dimensional Teichmüller space. 相似文献
19.
Dimitrios Betsakos 《Journal d'Analyse Mathématique》1999,79(1):201-214
We solve an extremal problem for the conformal capacity of certain space condensers. The extremal condenser is conformally
equivalent to Teichmüller’s ring. As an application, we give a dimension-free estimate for the minimal conformal capacity
of the condensers with platesE, F such thata, b ∈ E,c, d ∈ F, wherea, b, c, d are given points in
. 相似文献
20.
We study the convergence of earthquake paths and horocycle paths in the Gardiner-Masur compactification of Teichmüller space. We show that an earthquake path directed by a uniquely ergodic or simple closed measured geodesic lamination converges to the Gardiner-Masur boundary. Using the embedding of flat metrics into the space of geodesic currents, we prove that a horocycle path in Teichmüller space, which is induced by a quadratic differential whose vertical measured foliation is unique ergodic, converges to the Gardiner-Masur boundary and to the Thurston boundary. 相似文献