Capacity convergence consequence of the Schoen–Yau zero mass stability conjecture

Let $\Omega_j$ be the isoperimetric regions associated with a sequence satisfying the hypotheses of the zero mass stability conjecture, and let $B_0(R)\subset{\mathbb E}^3$ be the Euclidean ball of radius $R$. Capacity convergence consequence. Under the hypotheses of that conjecture, the capacity of $\Omega_j$ semi-converges to the capacity of $B_0(R)$, in the sense considered by Jauregui, Perales, and Portegies.

This is proposed as a consequence of the conjectured geometric stability and the known semicontinuity results for capacity; the source leaves it as an open question.