## On Quadratic Differential Metrics on a Closed Riemann Surface

J. Math. Sci. Univ. Tokyo
Vol. 21 (2014), No. 2, Page 221–234.

Sun, Zongliang
On Quadratic Differential Metrics on a Closed Riemann Surface
We study properties of the space of quadratic differential metrics on a closed Riemann surface of genus $g \geq 2.$ 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.