# Applications of Alexandrov spaces to Riemannian geometry

I am an expert neither in Riemannian geometry nor in Alexandrov spaces. I am wondering what are the applications of Alexandrov spaces to more classical Riemannian geometry.

For example one can show that there exist only finitely many homeomorphisms types of closed smooth Riemannian manifolds of dimension $n$, diameter at most $D$, sectional curvature at least $\kappa$, and volume at least $v>0$ for fixed parameters $n,D,\kappa,v$. The proof uses the Gromov compactness theorem and the Perelman stability theorem.