3 problems

Let $C$ be a convex body, and let $T^w_C(K,\theta)$ denote the associated directional Chebyshev constants constructed using a global monomial ordering satisfying the conditions des…

Let $T=\{z\in\mathbb C:|z|=1\}$, let $\xi_k=e^{2\pi i k/n}$ for $k=1,\dots,n$, and let $M_n^p(T)$ denote the maximal Chebyshev constant for $n$ points on $T$ associated with the ke…

Uniform distribution conjecture. For every such $f$, $M_f(\theta_1,\dots,\theta_n)$ is maximised when the points are uniformly distributed on $[0,2\pi)$.