3 problems

Large-aspect-ratio minimizer conjecture. For $L/H \geqslant L_1$, there exists a two-dimensional minimizer $u_L$ such that $E_0[u_L]$ is lower than the minimum energy achieved over…

Intermediate-regime minimizer conjecture. For $L/Hin (L_0,L_1)$, the critical point constructed in the proof of Theorem textnormal{not1d} is a minimizer of $E_0$.

Small-aspect-ratio minimizer conjecture. For $0 < L/H < L_0$, the one-dimensional minimizer from Theorem 1 is a unique minimizer of $E_0$ among all two-dimensional competitors.