Analysis of the Wu metric .2. The case of non-convex Thullen domains

Abstract

We present an explicit description of the Wu invariant metric on the non-convex Thullen domains. We show that the Wu invariant Hermitian metric, which in general behaves as nicely as the Kobayashi metric under holomorphic mappings, enjoys better regularity in this case. Furthermore, we show that the holomorphic curvature of the Wu metric is bounded from above everywhere by -1/2. This leads the Wu metric to be a natural solution to a conjecture of Kobayashi in the case of non-convex Thullen domains.