2 problems

Let $\mathbf{K}$ be a compact convex set of area $1$, let $\lambda>0$, and suppose that $\operatorname{argmax}\Phi_{\lambda,\mathbf{K}}$ consists of the single element $C^\star$, w…

Let $\mathbf{K}$ be a compact convex set of area $1$, let $\lambda>0$, and let $C^\star$ be the unique element of $\operatorname{argmax}\Phi_{\lambda,\mathbf{K}}$, where … Let…