  We characterization hyperbolic metrics on compact surfaces with boundary
using a variational principle. As a consequence, a new parametrization of the
Teichmuller space of compact surface with boundary is produced. In the new
parametrization, the Teichmuller space becomes an open convex polytope. It is
conjectured that the Weil-Petersson symplectic form can be expressed explicitly
in terms of the new coordinate.
