Reverse Loomis-Whitney inequalities via isotropicity

Alonso Gutiérrez, David (Universidad de Zaragoza) ; Brazitikos, Silouanos

Resumen: Given a centered convex body $ K\subseteq \mathbb{R}^n$, we study the optimal value of the constant $ \tilde {\Lambda }(K)$ such that there exists an orthonormal basis $ \{w_i\}_{i=1}^n$ for which the following reverse dual Loomis-Whitney inequality holds:
$\displaystyle \vert K\vert^{n-1}\leqslant \tilde {\Lambda }(K)\prod _{i=1}^n\vert K\cap w_i^\perp \vert.$
We prove that $ \tilde {\Lambda }(K)\leqslant (CL_K)^n$ for some absolute $ C>1$ and that this estimate in terms of $ L_K$, the isotropic constant of $ K$, is asymptotically sharp in the sense that there exist another absolute constant $ c>1$ and a convex body $ K$ such that $ (cL_K)^n\leqslant \tilde {\Lambda }(K)\leqslant (CL_K)^n$. We also prove more general reverse dual Loomis-Whitney inequalities as well as reverse restricted versions of Loomis-Whitney and dual Loomis-Whitney inequalities.

Idioma: Inglés

DOI: 10.1090/proc/15265

Año: 2021

Publicado en: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY 149, 2 (2021), 833 - 844
ISSN: 0002-9939

Factor impacto JCR: 0.971 (2021)

Categ. JCR: MATHEMATICS rank: 166 / 333 = 0.498 (2021) - Q2 - T2
Categ. JCR: MATHEMATICS, APPLIED rank: 207 / 267 = 0.775 (2021) - Q4 - T3

Factor impacto CITESCORE: 1.7 - Mathematics (Q3)

Factor impacto SCIMAGO: 0.891 - Mathematics (miscellaneous) (Q1) - Applied Mathematics (Q1)

Tipo y forma: Article (PostPrint)

Área (Departamento): Área Análisis Matemático (Dpto. Matemáticas)