Characterizing candidates for Cannon's conjecture from geometric measure theory.

We show that recent work of Song implies that torsion‐free hyperbolic groups with Gromov boundary S2$S^2$ arerealized as fundamental groups of closed 3‐manifolds of constant negative curvature if and only if the solution to an associated spherical Plateau problem for group homology is isometric to such a 3‐manifold, and suggest some related questions. [ABSTRACT FROM AUTHOR]