147761 20250103153613.0 doi 10.1090/proc/15265 sideral 121283 ART-2021-121283 eng Alonso Gutiérrez, David Universidad de Zaragoza (orcid)0000-0003-1256-3671 Reverse Loomis-Whitney inequalities via isotropicity 2021 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. Access copy available to the general public Unrestricted info:eu-repo/semantics/openAccess All rights reserved http://www.europeana.eu/rights/rr-f/ 0.971 2021 MATHEMATICS 166 / 333 = 0.498 2021 Q2 T2 MATHEMATICS, APPLIED 207 / 267 = 0.775 2021 Q4 T3 0.891 2021 Mathematics (miscellaneous) 2021 Q1 Applied Mathematics 2021 Q1 1.7 2021 info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion Brazitikos, Silouanos 2006 015 Universidad de Zaragoza Dpto. Matemáticas Área Análisis Matemático 149, 2 (2021), 833 - 844 Proc. Am. Math. Soc. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY 0002-9939 353555 http://zaguan.unizar.es/record/147761/files/texto_completo.pdf Postprint 1181020 http://zaguan.unizar.es/record/147761/files/texto_completo.jpg?subformat=icon icon Postprint oai:zaguan.unizar.es:147761 articulos driver 2025-01-03-13:20:59 ARTICLE