Current browse context:
math.FA
Change to browse by:
References & Citations
Mathematics > Functional Analysis
Title: A New Excluding Condition towards the Soprunov-Zvavitch conjecture on Bezout-type inequalities
(Submitted on 2 Feb 2023 (v1), last revised 4 Feb 2023 (this version, v2))
Abstract: In 2015, I. Soprunov and A. Zvavitch have shown how to use the Bernstein-Khovanskii-Kushnirenko theorem to derive non-negativity of a certain bilinear form $F_{\Delta}$, defined on (pairs of) convex bodies. Together with C. Saroglou, they proved non-negativity of $F_K$ characterizes simplices, among all polytopes. It is conjectured the characterization further holds among all convex bodies. Towards this conjecture, several necessary conditions on $K$ (for non-negativity of $F_K$), were derived. We give a new necessary condition, expressed with isoperimetric ratios, which provides a further step towards a (conjectural) characterization of simplices among a certain subclass of convex bodies.
Submission history
From: Maud Szusterman [view email][v1] Thu, 2 Feb 2023 16:47:21 GMT (64kb,D)
[v2] Sat, 4 Feb 2023 23:14:53 GMT (64kb,D)
Link back to: arXiv, form interface, contact.