7 problems

Extension conjecture. Theorem 3 should hold without the hypothesis $H\geq 0$.

Non-collapsing conjecture. The non-existence of singular solutions to the homotopic Plateau problem should be sufficient to exclude collapsing; equivalently, it should guarantee no…

The exact hydrodynamic closure of a kinetic model modifies the entropy so as to ensure pure dissipation in the hydrodynamic variables; this is viewed as a non-local extension of Ko…

Minimality conjecture. Generalized minimizers for the soap-film capillarity problem are minimal among the relaxed class $\mathcal{K}$ of possibly collapsed soap films. This concern…

Let $(K_h,E_h)\to S$ be the minimal surfaces limit described in Theorem, where $S$ is a minimizer of the Plateau problem $\ell$. The singularity-accumulation conjecture. Low-codime…

Assume the same capillary-surface setting with $n=2$, where $\Omega$ has a corner at $P$ of angular size $2\alpha$ and $\gamma(x)\to\gamma_{0}$ as $x\to P$ along $\partial\Omega$.…

Assume $n=2$. Let $\kappa\ge 0$, let $\Omega\subset\mathbb{R}^{2}$ have a corner at $P\in\partial\Omega$ of angular size $2\alpha$, where $\alpha\in\left(0,\frac{\pi}{2}\right)$, a…