We introduce an asymptotic quantity that counts area-minimizing surfaces in negatively curved closed 3-manifolds and show that quantity to only be minimized, among all metrics of sectional curvature , by the hyperbolic metric.
"Counting minimal surfaces in negatively curved 3-manifolds." Duke Math. J. 171 (8) 1615 - 1648, 1 June 2022. https://doi.org/10.1215/00127094-2021-0057