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Extemizers in Soprunov and Zvavitch's Bezout inequalities for mixed volumes

Maud Szusterman

Published 2023 in Unknown venue

ABSTRACT

In [SZ], Soprunov and Zvavitch have translated the Bezout inequalities (from Algebraic Geometry) into inequalities of mixed volumes satisfied by the simplex. They conjecture this set of inequalities characterizes the simplex, among all convex bodies in R^n. Together with Saroglou, they proved the characterization among all polytopes [SSZ1] and, for a larger set of inequalities, among all convex bodies [SSZ2]. The conjecture remains open for n \geq 4. In this work, we investigate necessary conditions on the structure of the boundary of a convex body K, for K to satisfy all inequalities. In particular, we obtain a new solution of the 3-dimensional case.

PUBLICATION RECORD

  • Publication year

    2023

  • Venue

    Unknown venue

  • Publication date

    2023-04-01

  • Fields of study

    Mathematics

  • Identifiers
    arXiv 2304.00366
  • External record

    Open on Semantic Scholar

  • Source metadata

    Semantic Scholar

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