Study of metric properties of Teichmuller spaces

我们研究了2维双曲旋涡的TeichMuller空间的度量性质，并研究了不连续群、2维和3维旋涡上的相关问题。1.利用圆锥点与角圆之间的距离将双曲圆锥曲面的Teichmuller空间刻画为实代数空间，并将其应用于求TeichMuller空间的整体参数化所需的测地长度函数的最小个数问题、映射类群的表示以及Riemann曲面的全纯族。与圆锥曲面底面上适当选取的闭合曲线有关的测地线长度函数提供了TeichMuller空间上的整体坐标系。我们用这些测地线长度函数表示了类似于Weil-Petersson二型的Wolpert公式的二型，并计算了一些模空间的体积。对所有非余紧算法进行分类。签名的Fuchsian群(0；theta_1，theta_2，theta_3，theta_4)。

We have studied metric properties of Teichmuller space of 2 dimensional hyperbolic orbifolds and related subjects on discontinuous groups and 2 and 3 dimensional orbifolds. We obtained the following results :1. Description of Teichmuller space of hyperbolic cone surfaces as a real algebraic space by using the distances between cone points and horocycles and its applications to the problem of finding the minimal number of geodesic length functions needed for a global parametrization of a Teichmuller space, the representation of mapping class groups and holomorphic families of Riemann surfaces.2. Geodesic length functions related to suitably chosen closed curves on the underlying surface of a cone surface supply a global coordinate-system on the Teichmuller space. We expressed the 2 form which is defined analogously to Wolpert's formula of Weil-Petersson 2-form in terms of these geodesic length functions and calculated the volumes of some moduli spaces.3. Classification of all non-cocompact arithmetic. Fuchsian groups of signature (0 ; theta_1, theta_2, theta_3, theta_4).