标题： 威尔-彼得森连接的扩展 显示英文标题

标题： Extension of the Weil-Petersson connection

摘要： 凸性性质的Weil-Petersson测地线在带有洞的黎曼曲面的Teichmüller空间中被研究。 对于压紧的双曲度量，给出了Weil-Petersson Levi-Civita联络的规范形式。 该规范形式用于建立边界空间中测地线的逼近。 结合这些考虑，建立了双曲度量下水平圆之间距离函数沿Weil-Petersson测地线的凸性。 显示英文摘要

摘要： Convexity properties of Weil-Petersson geodesics on the Teichm\"{u}ller space of punctured Riemann surfaces are investigated. A normal form is presented for the Weil-Petersson Levi-Civita connection for pinched hyperbolic metrics. The normal form is used to establish approximation of geodesics in boundary spaces. Considerations are combined to establish convexity along Weil-Petersson geodesics of the functions the distance between horocycles for a hyperbolic metric.