  Let $\cM_{g,n}$ be the moduli space of Riemann surfaces of genus $g$ with $n$
punctures.
  From a complex perspective, moduli space is hyperbolic. For example,
$\cM_{g,n}$ is abundantly populated by immersed holomorphic disks of constant
curvature -1 in the Teichm\"uller (=Kobayashi) metric.
  When $r=\dim_{\cx} \cM_{g,n}$ is greater than one, however, $\cM_{g,n}$
carries no complete metric of bounded negative curvature. Instead, Dehn twists
give chains of subgroups $\zed^r \subset \pi_1(\cM_{g,n})$ reminiscent of flats
in symmetric spaces of rank $r>1$.
  In this paper we introduce a new K\"ahler metric on moduli space that
exhibits its hyperbolic tendencies in a form compatible with higher rank.
