Thick-thin decomposition for quadratic differentials
arXiv:1407.4789
Abstract
We compare the flat geometry associated to a quadratic differential with the hyperbolic geometry associated to the underlying Riemann surface. We show that if a curve is contained in a thick subsurface, then its hyperbolic length is comparable to its flat length times the flat size of the subsurface.
This is an old paper that has been already published in 2007 in Math. Research Letters. I am posting it to the arxiv for completeness