Dedicated to Professor LU QiKeng on the occasion of his 80th birthday.

                                       Abstract

In this paper we briefly survey our recent results about the Mumford goodness of several
canonical metrics on the moduli spaces of Riemann surfaces. We will also prove the dual
Nakano negativity of the Weil-Petersson metric. As applications of these results we will deduce
certain important results about the L2-cohomology groups of the logarithmic tangent bundle
over the compactified moduli spaces.