Abstract
Convexity properties of Weil-Petersson (WP) 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
Citation
Scott A. Wolpert. "Extension of the Weil-Petersson connection." Duke Math. J. 146 (2) 281 - 303, 1 February 2009. https://doi.org/10.1215/00127094-2008-066
Information