Convex Polytopes, Dihedral Angles, Mean Curvature and Scalar Curvature
Abstract
We approximate boundaries of convex polytopes by smooth hypersurfaces Y=Y with positive mean curvatures and, by using basic geometric relations between the scalar curvatures of Riemannin manifolds and the mean curvatures of their boundaries, establish lower bound on the dihedral angles of these polytopes.
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