2 problems

Extension conjecture. The same bound should hold for every $s\geq1$: there should exist a finite $c(s)$, with $c(s)\to\infty$ as $s\to\infty$, such that

Nam's radial-measure conjecture. The infimum defining $\beta_2$ is achieved by radially symmetric probability measures $\mu$; equivalently, $\beta_2$ can be calculated using only r…