TY - GEN A1 - Hildebrandt, Klaus A. A1 - Polthier, Konrad A1 - Wardetzky, Max T1 - On the convergence of metric and geometric properties of polyhedral surfaces N2 - We provide conditions for convergence of polyhedral surfaces and their discrete geometric properties to smooth surfaces embedded in R^3. The notion of totally normal convergence is shown to be equivalent to the convergence of either one of the following: surface area, intrinsic metric, and Laplace-Beltrami operators. We further show that totally normal convergence implies convergence results for shortest geodesics, mean curvature, and solutions to the Dirichlet problem. This work provides the justifi- cation for a discrete theory of differential geometric operators defined on polyhedral surfaces based on a variational formulation. Y1 - 2005 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/273 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-2733 ER -