# Shephard's inequalities, Hodge-Riemann relations, and a conjecture of Fedotov

@inproceedings{Handel2021ShephardsIH, title={Shephard's inequalities, Hodge-Riemann relations, and a conjecture of Fedotov}, author={Ramon van Handel}, year={2021} }

A well-known family of determinantal inequalities for mixed volumes of convex bodies were derived by Shephard from the Alexandrov-Fenchel inequality. The classic monograph Geometric Inequalities by Burago and Zalgaller states a conjecture on the validity of higher-order analogues of Shephard’s inequalities, which is attributed to Fedotov. In this note we disprove Fedotov’s conjecture by showing that it contradicts the Hodge-Riemann relations for simple convex polytopes. Along the way, we make… Expand

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