Communications in Analysis and Geometry
Volume 25 (2017)
The diffeomorphism type of manifolds with almost maximal volume
Pages: 243 – 267
The smallest $r$ so that a metric $r$–ball covers a metric space $M$ is called the radius of $M$. The volume of a metric $r$-ball in the space form of constant curvature $k$ is an upper bound for the volume of any Riemannian manifold with sectional curvature $\geq k$ and radius $\leq r$. We show that when such a manifold has volume almost equal to this upper bound, it is diffeomorphic to a sphere or a real projective space.
diffeomorphism stability, Alexandrov geometry
2010 Mathematics Subject Classification
Paper received on 14 November 2013.