Vol. 197, No. 1, 2001

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An extension of Wolpert’s derivative formula

Caroline Series

Vol. 197 (2001), No. 1, 223–239
Abstract

A well known formula of Wolpert expresses the derivative of length of a geodesic γ on a hyperbolic surface with respect to the Fenchel Nielsen twist about a fixed simple geodesic C as a sum of the cosines of the intersection angles between the two curves. We derive an analogous formula for the derivative of the length of γ with respect to variation of the length of the fixed curve C.

Milestones
Received: 14 December 1998
Published: 1 January 2001
Authors
Caroline Series
Mathematics Institute
Warwick University
Coventry CV4 7AL
United Kingdom