Corpus ID: 237492041

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

  title={Shephard's inequalities, Hodge-Riemann relations, and a conjecture of Fedotov},
  author={Ramon van Handel},
  • R. Handel
  • Published 11 September 2021
  • Mathematics
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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