Konvexe Bereiche kleinster Oberfläche bei gegebener Dicke

Abstract

A till now unconfirmed conjecture is proved analytically: The balls are in ${\mathbb{E}}^n(n\ge 3)$ the single convex domains of given thickness with smallest surface area. The proof is effected by means of a generalized duality theory of restricted multidimensional variational problems in parametric form.