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arXiv · 1612.07753

Piecewise Flat Extrinsic Curvature

Rory Conboye
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Abstract

Discretizations of the mean curvature and extrinsic curvature components are constructed on piecewise flat simplicial manifolds, giving approximations for smooth curvature values in a mostly mesh-independent way. These constructions are given in combinatoric form in terms of the extrinsic hinge angles, the intrinsic structure of the piecewise flat manifold and a choice of dual tessellation, and can be viewed as the average of $n$-volume integrals. The constructions are also independent of the manifold dimension.

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Rory Conboye. 2016-12-22. Piecewise Flat Extrinsic Curvature. https://arxiv.org/abs/1612.07753

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