منابع مشابه
Average Curvatures of Weil-Petersson Geodesics In Teichmüller Space
Every point in Teichmüller space is a hyperbolic metric on a given Riemann surface, therefore, a Weil-Petersson geodesic in Teichmüller space can be viewed as a 3-manifold. We investigate the sectional curvatures of this 3-manifold, with a natural metric. We obtain explicit formulas for the curvature tensors of this metric, and show that the “average”s of them are zero, and hence the geometry o...
متن کاملGrowth of the Weil-petersson Inradius of Moduli Space
In this paper we study the systole function along WeilPetersson geodesics. We show that the square root of the systole function is uniform Lipschitz on the Teichmüller space endowed with the Weil-Petersson metric. The inradius of a metric space is the largest radius of metric balls contained in the interior of the metric space. As applications of the result above, we study the growth of the Wei...
متن کاملWeil-Petersson Geometry of the Universal Teichmüller Space
The universal Teichmüller space T (1) is the simplest Teichmüller space that bridges spaces of univalent functions and general Teichmüller spaces. It was introduced by Bers [Ber65, Ber72, Ber73] and it is an infinite-dimensional complex Banach manifold. The universal Teichmüller space T (1) contains Teichmüller spaces of Riemann surfaces as complex submanifolds. The universal Teichmüller space ...
متن کاملThe Weil-petersson Hessian of Length on Teichmüller Space
We present a brief but nearly self-contained proof of a formula for the Weil-Petersson Hessian of the geodesic length of a closed curve (either simple or not simple) on a hyperbolic surface. The formula is the sum of the integrals of two naturally defined positive functions over the geodesic, proving convexity of this functional over Teichmuller space (due to Wolpert (1987)). We then estimate t...
متن کاملClassification of Weil-petersson Isometries
This paper contains two main results. The first is the existence of an equivariant Weil-Petersson geodesic in Teichmüller space for any choice of pseudo-Anosov mapping class. As a consequence one obtains a classification of the elements of the mapping class group as WeilPetersson isometries which is parallel to the Thurston classification. The second result concerns the asymptotic behavior of t...
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ژورنال
عنوان ژورنال: American Journal of Mathematics
سال: 2018
ISSN: 1080-6377
DOI: 10.1353/ajm.2018.0023