Many interesting classes of Riemannian manifolds are precompact in the Gromov ... In particular, we will study manifolds, their diffeomorphisms and embeddings, and positive scalar curvature metrics on ...

Other goals include structure results for singular Riemannian foliations in nonnegative curvature and a differentiable diameter pinching theorem. Hamilton's Ricci flow is a (weakly parabolic) ...

Mathematicians already knew that the way in which curvature varies from place to place inside a ‘Riemannian manifold’ — the mathematical jargon for curved space — determines the shortest ...