10 citations · 17 across the 9 of their papers we have counts for
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math.MG2007
Convexity of Hypersurfaces in Spherical Spaces
Konstantin Rybnikov
A spherical set is called convex if for every pair of its points there is at least one minimal geodesic segment that joins these points and lies in the set. We prove that for n >=…
cs.CG2007★ 1 cited
An Efficient Local Approach to Convexity Testing of Piecewise-Linear Hypersurfaces
Konstantin Rybnikov
We show that a closed piecewise-linear hypersurface immersed in () is the boundary of a convex body if and only if every point in the interior of each -face ha…
math.MG2007★ 10 cited
Perfect Delaunay Polytopes in Low Dimensions
Mathieu Dutour, Robert Erdahl, Konstantin Rybnikov
A lattice Delaunay polytope is known as perfect if the only ellipsoid, that can be circumscribed about it, is its Delaunay sphere. Perfect Delaunay polytopes are in one-to-one corr…