Characterizing candidates for Cannon's Conjecture from Geometric Measure Theory

Abstract

We show that recent work of Song implies that torsion-free hyperbolic groups with Gromov boundary $S^2$ are realized 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.

arXiv comment7 pages. This is the accepted version of the following article: Cheetham-West, T. and Nolte, A. (2023), Characterizing candidates for Cannon's conjecture from geometric measure theory. Bull. London Math. Soc.. https://doi.org/10.1112/blms.12814, which has been published in final form at http://doi.org/10.1112/blms.12814