In Riemannian geometry, Gromov's compactness theorem states that the set of Riemannian manifolds with Ricci curvature ≥ c and diameter ≤ D is pre-compact in the Gromov-Hausdorff metric. It was proved by Mikhail Gromov. In differential geometry, Riemannian geometry is the study of smooth manifolds with Riemannian metrics, i. ... In differential geometry, the Ricci curvature tensor is (0,2)-valent tensor, obtained as a trace of the full curvature tensor. ... Diameter is an AAA (authentication, authorization and accounting) protocol for applications such as network access or IP mobility. ... This is a glossary of some terms used in the branch of mathematics known as topology. ... Gromov-Hausdorff convergence is a notion for convergence of metric spaces which is a generalization of Hausdorff convergence. ... Mikhail Leonidovich Gromov Russian: Михаил Леонидович Громов (born December 23, 1943, also known as Mikhael Gromov, Michael Gromov, or Misha Gromov) is a mathematician known for important contributions in many different areas of geometry, especially metric geometry, symplectic geometry, and geometric group theory. ...