Graduate School of Mathematical Sciences, The University of Tokyo
Abstract
We study properties of the space of quadratic differential metrics on a closed Riemann surface of genus g ≥ 2. First, we introduce a natural metric on this space defined via length distortions which is proper and compact. Second, we study topological properties of this space and show equivalence of various convergences. Besides, we relate the preceding metric to another metric which is obtained via global Lipschitz constants
