Hi All, I am trying to figure out the details on giving a surface S a hyperbolic metric with geodesic boundary, i.e., a metric of constant sectional curvature -1 so that the (manifold) boundary components, i.e., a collection of disjoint simple-closed curves are geodesics under this metric. So far I know: 1) There are genus constraints for the surface. Does this have to see with Gauss-Bonnet? 2) Something; not sure exactly what, can be done by gluing pairs-of-pants http://en.wikipedia.org/wiki/Pair_of_pants_(mathematics [Broken]) but not fully sure how this works. Not much more. Any ideas, refs., please?