Extension of Theorem 3 to negative mean curvature

The discussion concerns capillary drops bounded by support planes, with $H$ denoting the constant mean curvature of the drop. The preceding theorem establishes uniqueness under the hypothesis $H\geq 0$, while the wedge case supplies uniqueness information when $H<0$.

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

The proposed extension would give uniqueness for the relevant disk-type capillary surfaces also when the mean curvature is negative. The paper presents this as a conjecture motivated by the transition from trihedral angles to wedges; no resolution is supplied here.