5 problems

Periodic replication conjecture. Without requiring $(\widetilde U,\widetilde V)$ to be a global minimizer or compactly supported in $\Omega$, one has

Three-dimensional Gamma-limit conjecture. For $n=3$ and $\rho\to0$, if $\zeta\in(\zeta_0,\zeta_1)$, the Gamma-limit of $F'_\rho$ is a quadratic form in the principal curvatures for…

Two-dimensional Gamma-limit conjecture. For $n=2$ and $\rho\to0$, if $\zeta\in(0,\zeta_1)$, the Gamma-limit of $F'_\rho$ is the elastica functional for closed $W^{2,2}$ curves in…

Three-dimensional asymptotic morphology conjecture. For $n=3$, fixed $\gamma>0$, and $\zeta>\zeta_0$,

Helfrich-limit conjecture. The Gamma-limit of the rescaled bilayer energy is the Helfrich energy.