3 problems

Chen–Gonzales–Goodman–Kang–Okoudjou's conjecture. If $p\in(p_{k-1},p_k]$ for $k=1,2,\ldots,d$, then $L_k^d$ minimizes the $p$-frame potential when $N=d+1$.

Let $E_2$ denote the second relaxation, or four-point bound, in the semidefinite hierarchy for energy minimization. For five particles on $S^2$, consider all completely monotonic p…

Let $E_s(\omega_N)$ denote the Riesz $s$-energy of a configuration $\omega_N\subset\mathbb{S}^2$, let $E_{\log}(\omega_N)$ denote its logarithmic energy, and let $\omega_N^{\log}$…