An Isodiametric Problem with Additional Constraints in Euclidean space R^3

Abstract

Let $C_{\hat{I}}¸$ be a circular cone in Euclidean space ${\mathbb{R}}^3$,which apex is the origin and apex angle of the cone is $\hat{I}¸\in \left(\ddot{I}€/3,\ddot{I}€\right)$. Let $M_{\hat{I}}¸$ be the class of compact convex domains in Euclidean space ${\mathbb{R}}^3$, which have diameter one, contains the origin and are included in $C_{\hat{I}}¸$. In this paper, we show that there is a unique compact convex domain with maximal volume and also we determine the shape of the above domain.

There are some mistakes in the paper and the results are not new