Lengthening deformations of singular hyperbolic tori

Abstract

Let $S$ be a torus with a hyperbolic metric admitting one puncture or cone singularity. We describe which infinitesimal deformations of $S$ lengthen (or shrink) all closed geodesics. We also study how the answer degenerates when $S$ becomes Euclidean, i.e. very small.

17 pages, 5 figures. To appear in: Annales de la faculté des sciences de Toulouse (volume dedicated to Michel Boileau's sixtieth birthday)