3 problems

For a ball of radius $R$, let $\mu_*$ be the minimum value of the isolated-droplet energy per unit volume and let $m_*$ be the largest volume among minimizers, while $m_{**}$ is th…

Let … for measurable sets $\Omega\subset\mathbb{R}^3$ of positive volume, and let $\Omega_*$ be a minimizer of $I$. Two sets are considered equivalent under the symmetries of the p…

Let E_{[?] denote the energy of a configuration in the liquid drop model at background density $[?]$, and consider minimizers in the dilute limit $[?]\to 0$. A minimizer is under…