A bound on local minima of arrangements that implies the upper bound theorem
The \(i\)-level of a simple arrangement of hyperplanes in \(E^ d\) is the boundary of the set of all points that are below at most \(i\) hyperplanes. Author proves an upper bound for the number of local minima of the \(i\)- level. From this he deduces by linear programming duality the Upper Bound Theorem for convex polytopes.
scientific article; zbMATH DE number 488285