Existence of free boundary minimal surfaces in spherical and hyperbolic balls

Establish that every geodesic ball in the hemisphere S^3_+ and in hyperbolic space H^3 contains free boundary minimal surfaces realizing every orientable topological type.

Background

By analogy with the Euclidean 3-ball, the authors expect analogous realization results in other space forms via appropriate eigenvalue optimization problems identified in recent work.

A proof would generalize the topological realization theorem beyond the Euclidean ball.