2 problems

Let $\varOmega$ be a convex body in $\mathbb{R}^m$, and for $\alpha>0$ let its $r^{\alpha-m}$-center be a point where the extreme value of the potential … is attained, with the rel…

Let $\varOmega$ be a convex body in $\mathbb{R}^m$. For $\alpha>0$, define … and call a point where this potential attains its relevant extreme value an $r^{\alpha-m}$-center. Uniq…