IASM Preprint Series 2022-04: Length minima for an infinite family of filling closed curves on a one-holed torus
ZHONGZI WANG AND YING ZHANG
Abstract. We explicitly find the minima as well as the minimum points of the geodesic length functions for the family of filling (hence non-simple) closed curves,
on a complete one-holed hyperbolic torus in its relative Teichmuller space, where a, b are simple closed curves on the one-holed torus which intersect once transversely. This provides concrete examples for the problem to minimize the geodesic length of a fixed filling closed curve on a complete hyperbolic surface of finite type in its relative Teichmuller space.