On a Problem of Gromov about Generalizing Alexandrov-Fenchel Inequality
Yuri Burda
TL;DR
This paper addresses Gromov's question on mixed volumes, providing an answer and revisiting key definitions and properties related to mixed volumes and discriminants in convex geometry.
Contribution
It offers a solution to a problem posed by Gromov concerning mixed volumes, expanding understanding in convex geometry and related inequalities.
Findings
Provides an answer to Gromov's question on mixed volumes
Revisits and clarifies properties of mixed volumes and discriminants
Enhances theoretical understanding of convex geometric inequalities
Abstract
In this note we give an answer to a question about mixed volumes asked by Gromov in his paper "Convex Sets and Kahler Manifolds". For reader's convenience we remind definitions and some of the properties of mixed volumes and mixed discriminants.
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Taxonomy
TopicsPoint processes and geometric inequalities · Algebraic Geometry and Number Theory · Geometry and complex manifolds