On the variation of a series on Teichmüller space

Greg McShane

Vol. 231 (2007), No. 2, 461–479

DOI: 10.2140/pjm.2007.231.461

Abstract

Using the Kerckhoff–Wolpert formula for the variation of the length of a geodesic along a Fenchel–Nielsen twist, we prove that a certain series defines a constant function.

Keywords

Riemann surfaces, moduli, geodesic lengths, length spectrum, Fenchel–Nielsen twist

Mathematical Subject Classification 2000

Primary: 51M25, 53C22

Milestones

Received: 23 February 2006

Revised: 8 February 2007

Accepted: 23 February 2007

Published: 1 June 2007