  In this paper, we prove that every strictly convex 3-ball with nonnegative
Ricci-curvature contains at least 3 embedded free-boundary minimal 2-disks for
any generic metric, and at least 2 solutions even without genericity
assumption. Our approach combines ideas from mean curvature flow, min-max
theory and degree theory. We also establish the existence of smooth
free-boundary mean-convex foliations. In stark contrast to our prior work in
the closed setting, the present result is sharp for generic metrics.
