Riemannian metrics on hyperbolic components (Yan Mary He - University of Oklahoma)

We introduce a Riemannian metric on certain hyperbolic components of the moduli space of rational maps, which is an analogue of the Weil-Petersson metric on Teichmuller spaces. We show that our metric on the space of quasi-Blaschke products is an extension of McMullen’s Weil-Petersson type metric on the space of Blaschke products and is degenerate along the purely imaginary directions. The talk is based on joint works with Hongming Nie, Homin Lee and Insung Park.