  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.
