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On exterior calculus and curvature in piecewise-flat manifolds (1212.0919v1)
Published 5 Dec 2012 in math.DG and gr-qc
Abstract: Simplicial, piecewise-flat discretizations of manifolds provide a clear path towards curvature analysis on discrete geometries and for solutions of PDE's on manifolds of complex topologies. In this manuscript we review and expand on discrete exterior calculus methods using hybrid domains. We then analyze the geometric structure of curvature operators in a piecewise-flat lattice.