Inequalities for volumes of simplices in terms of their faces (Q1275292)

The authors generalize some known geometric inequalities referring to \(n\)-dimensional simplicies in Euclidean \(n\)-space, \(n\geq 2\). More precisely, they obtain an inequality involving the volume and the product of \(k\)-volumes of \(k\)-dimensional faces of an \(n\)-simplex, \(k\in\{1,2, \dots, n\}\). On that basis, they derive generalizations of two inequalities maximizing the volume of one or two \(n\)-simplicies in terms of their edge lengths. The obtained inequalities yield also (in form of the equality cases) characterizations of regular \(n\)-simplices.