On the Classical, Penrose, and Reverse Isoperimetric Inequalities in Black Holes: Insights From AdS to Flat Riemannian Backgrounds

A collection of evidence is presented showing that the conjectured reverse isoperimetric inequality (RII) for asymptotically anti-de Sitter (AdS) as well as de Sitter (dS) black holes, ${\cal R}_\text{RII} \ge 1$, is of fundamental importance and its violation (${\cal R}_\text{RII} < 1$) gives rise