5 problems

Let $\widehat{\Sigma}_i\in\mathcal{K}_{\omega_0}$ for $1\leqslant i\leqslant n+1$, where $\mathcal{K}_{\omega_0}$ is the class of anisotropic $\omega_0$-capillary convex bodies, an…

Let $f$ be a nonparametric capillary surface, represented as a function over a domain with a corner, and let $\theta_0^1,\theta_0^2$ be the corresponding contact angles. Suppose th…

Let $\mathbb{B}^3$ be the unit ball in $\mathbb{R}^3$, and let $\mathbb{A}_{2n}(\mu)$ denote the minimal annuli constructed in Theorem. Choe's conjecture. Any embedded capillary mi…

Let $\mathbb{A}_n(\mu)$ be the capillary minimal annuli in $\mathbb{B}^3$ constructed in Theorem, where $n>1$ and $\mu\geq 0$. A conjecture is that these annuli are embedded for ev…

Heintze–Karcher conjecture. The inequalities