I am looking for applications of the notion of Gromov-Hausdorff convergence to prove theorems that a priori have nothing to do with it. Examples that I am aware of (thanks to wikipedia and google):
What are more examples? Ideally they would be along the lines of Gromov's theorem, or proofs of geometric facts, but I'm interested to hear about anything.
As a subquestion, are there interesting applications of Gromov's compactness theorem to prove results about manifolds with bounded Ricci which have nothing to do with GH convergence?