On the curvature of two-dimensional singular Regge lattices

Details On the curvature of two-dimensional singular Regge lattices On the curvature of two-dimensional singular Regge lattices

May 1997

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1997cqgra..14.1079o&link_type=abstract

Classical and Quantum Gravity, Volume 14, Issue 5, pp. 1079-1097 (1997).

Physics

Scientific paper

We consider geodesic approximation of a two-dimensional Riemannian manifold, M, with a singular Regge lattice K and, in particular, relations between classical continuum curvature power actions 0264-9381/14/5/014/img1 and corresponding lattice actions. By the singular Regge lattice we mean a triangulated piecewise flat space having very thin triangles. It is shown that the continuum actions are well approximated by the lattice actions in the sense of measures, provided that the edge lengths of K are small, independently of whether very thin triangles are contained in K or not.

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