ON THE CURVATURE OF 2-DIMENSIONAL SINGULAR REGGE-LATTICES

We consider geodesic approximation of a two-dimensional Riemannian man ifold, M, with a singular Regge lattice K and, in particular, relation s between classical continuum curvature power actions integral R-k roo t gd(2)s and corresponding lattice actions. By the singular Regge latt ice we mean a triangulated piecewise Rat space having very thin triang les. It is shown that the continuum actions are well approximated by t he lattice actions in the sense of measures, provided that the edge le ngths of K are small, independently of whether very thin triangles are contained in K or not.