Extension of the Weil-Petersson connection

Abstract

Convexity properties of Weil-Petersson geodesics on the Teichmüller 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.

References in corpus (3)

• Geometry of the Weil-Petersson completion of Teichmüller space
• Stable curves and screens on fatgraphs
• Behavior of geodesic-length functions on Teichmueller space

Cited by in corpus (2)

• Understanding Weil-Petersson curvature
• The Weil-Petersson Hessian of Length on Teichmuller Space