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math.MG2020
Minkowski type theorems for convex sets in cones
Rolf Schneider
Minkowski's classical existence theorem provides necessary and sufficient conditions for a Borel measure on the unit sphere of Euclidean space to be the surface area measure of a c…
math.MG2020
Random Gale diagrams and neighborly polytopes in high dimensions
Rolf Schneider
Taking up a suggestion of David Gale from 1956, we generate sets of combinatorially isomorphic polytopes by choosing their Gale diagrams at random. We find that in high dimensions,…