5 problems

Let $U$ and $R$ be domains in the setting of Theorem, let $z$ be the specified starting point, and write $\tau_U$, $\tau_R$, $\tau_{U^+}$, and $\tau_{R^+}$ for the corresponding fi…

Let $\Omega$ be a bounded domain and let $H$ be a polarizer. The reverse Faber–Krahn conjecture. … The inequality is immediate in the cases discussed in the source when the transfi…

Let $E$subset ${\mathbb R}^2$ be compact and let $H$ be a polarizer. The polarization monotonicity conjecture. … Moreover, equality holds only if $P_H(E)\cong E$ or…

Let $({\mathcal L}^0,\mathbf e)$ be nondegenerate and strictly admissible. For generic admissible $({\mathcal L},\mathbf e)$ satisfying the partial symmetry hypothesis, with…

Let $({\mathcal L},{\mathbf e})$ satisfy the appropriate nondegeneracy and admissibility hypotheses, and suppose that $\mathcal L$ satisfies the partial symmetry hypothesis. A maxi…