Convexity of length functions and Thurston's shear coordinates

Abstract

We show that the length function of a measured geodesic lamination is convex in Thurston's shear coordinates over Teichmüller space and strictly convex for generic laminations. We give some consequences of this result in the context of Thurston's asymmetric metric on Teichmüller space.

43 pages, 14 figures

References in corpus (1)

• Shearing coordinates and convexity of length functions on Teichmueller space

Cited by in corpus (1)

• Derivatives of length functions and shearing coordinates on teichm{ü}ller spaces