Duke Mathematical Journal

Extension of the Weil-Petersson connection

Scott A. Wolpert

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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

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Duke Math. J., Volume 146, Number 2 (2009), 281-303.

First available in Project Euclid: 5 January 2009

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Zentralblatt MATH identifier

Primary: 32G15: Moduli of Riemann surfaces, Teichmüller theory [See also 14H15, 30Fxx]
Secondary: 20H10: Fuchsian groups and their generalizations [See also 11F06, 22E40, 30F35, 32Nxx] 30F60: Teichmüller theory [See also 32G15]


Wolpert, Scott A. Extension of the Weil-Petersson connection. Duke Math. J. 146 (2009), no. 2, 281--303. doi:10.1215/00127094-2008-066. https://projecteuclid.org/euclid.dmj/1231170941

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