doi:10.1090/proc/15265engAlonso Gutiérrez, DavidBrazitikos, SilouanosReverse Loomis-Whitney inequalities via isotropicityART-2021-121283Given 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.2021http://zaguan.unizar.es/record/14776110.1090/proc/15265http://zaguan.unizar.es/record/147761oai:zaguan.unizar.es:147761PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY 149, 2 (2021), 833 - 844All rights reservedhttp://www.europeana.eu/rights/rr-f/info:eu-repo/semantics/openAccess