9 papers · 1 filter
Local Topology of Riemannian Manifolds with Lower Intermediate Ricci Curvature Bounds
Philipp Reiser, Masoumeh Zarei
We prove a vanishing theorem for the local Betti numbers of closed, -dimensional Riemannian manifolds with a lower volume bound, an upper diameter bound, and a lower intermediat…
Precompactness for homogeneous Einstein metrics on torus bundles
Anusha M. Krishnan, Vincent P. N. Wolff, Masoumeh Zarei
We prove a precompactness result for homogeneous Einstein metrics on the set of homogeneous torus bundles over a common base. This set can contain infinite families of compact simp…
Ricci Flow Preserves Positive Sectional Curvature on Homogeneous Spheres
Jason DeVito, David González-Álvaro, Masoumeh Zarei
We prove that the Ricci flow preserves positive sectional curvature on homogeneous spheres and complex projective spaces. In conjunction with prior results, this completes the clas…
Ricci flow from singular spaces with bounded curvature
Diego Corro, Masoumeh Zarei, Adam Moreno
We show the existence of a solution to the Ricci flow with a compact length space of bounded curvature, i.e., a space that has curvature bounded above and below in the sense of Ale…
On the Geometry and Topology of Positively Curved Eschenburg Orbifolds
Dennis Wulle, Masoumeh Zarei
The present article explores the relationship between positive sectional curvature and the geometric and topological properties of Eschenburg -orbifolds. First, we prove that po…
Positive sectional curvature is not preserved under the Ricci flow in dimensions seven and thirteen
David González-Álvaro, Masoumeh Zarei
We prove that there exist -invariant metrics on Aloff-Wallach spaces , as well as -invariant metrics on the Berger space ,…