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

DOI10.1007/978-3-031-26300-2_13zbMATH Open1548.52009MaRDI QIDQ6608554

Ramon van Handel

Publication date: 20 September 2024

zbMATH Keywords

mixed volumesAlexandrov-Fenchel inequalityHodge-Riemann relations for convex polytopesShephard's inequalities

Mathematics Subject Classification ID

Toric varieties, Newton polyhedra, Okounkov bodies (14M25) Inequalities and extremum problems involving convexity in convex geometry (52A40) Mixed volumes and related topics in convex geometry (52A39)

Cites Work

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• On Hodge-Riemann relations for translation-invariant valuations
• On simple polytopes
• Volumen und Oberfläche.
• Mixed Hodge-Riemann bilinear relations in the linear situation
• The extremals of Minkowski's quadratic inequality
• Kotrbatý's theorem on valuations and geometric inequalities for convex bodies
• The mixed Hodge-Riemann bilinear relations for compact Kähler manifolds
• Zur Theorie der gemischten Volumina von konvexen Körpern. IV: Die gemischten Diskriminanten und die gemischten Volumina.
• From harmonic analysis of translation-invariant valuations to geometric inequalities for convex bodies
• Inequalities between mixed volumes of convex sets
• An analogue of the Hodge-Riemann relations for simple convex polytopes
• COMBINATORIAL APPLICATIONS OF THE HODGE–RIEMANN RELATIONS
• Mixed volumes and the Bochner method
• Convex Bodies The Brunn-MinkowskiTheory

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