Bodies of constant brightness
The author deals with the class of convex bodies of revolution in \(\mathbb{R}^n\) having a prescribed constant brightness. He proves that the \(n\)-dimensional Blaschke-Firey body in this class is the unique (up to rigid motion) body of minimal volume there. The Blaschke-Firey body is a natural generalization, due to Firey, of the Reuleaux triangle and the 3-dimensional body of constant brightness constructed by Blaschke in 1916 [\textit{W. Blaschke}, `Kreis und Kugel.' New York (1949; Zbl 0041.08802); pp. 151-154].
scientific article; zbMATH DE number 1186707