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Inequalities Between Mixed Volumes Of Convex Bodies: Volume Bounds For The Minkowski Sum, Gennadiy Averkov, Christopher Borger, Ivan Soprunov

Mathematics and Statistics Faculty Publications

n the course of classifying generic sparse polynomial systems which are solvable in radicals, Esterov recently showed that the volume of the Minkowski sum P1++Pd of d-dimensional lattice polytopes is bounded from above by a function of order O(m2d), where m is the mixed volume of the tuple (P1,,Pd). This is a consequence of the well-known Aleksandrov-Fenchel inequality. Esterov also posed the problem of determining a sharper bound. We show how additional relations between mixed volumes can be employed to improve the bound to O(md), which is asymptotically sharp. We furthermore prove a sharp exact upper bound in dimensions 2 …