7 papers
The covering spectrum of a compact length space
Christina Sormani, Guofang Wei
We define a new spectrum for compact length spaces and Riemannian manifolds called the "covering spectrum" which roughly measures the size of the one dimensional holes in the space…
Universal Covers for Hausdorff Limits of Noncompact Spaces
Christina Sormani, Guofang Wei
We prove that if is the Gromov-Hausdorff limit of a sequence of complete manifolds, , with a uniform lower bound on Ricci curvature then has a universal cover.
The codimension one homology of a complete manifold with nonnegative Ricci curvature
Zhongmin Shen, Christina Sormani
In this paper we prove that a complete noncompact manifold with nonnegative Ricci curvature has a trivial codimension one homology unless it is a split or flat normal bundle over a…
On Loops Representing Elements of the Fundamental Group of a Complete Manifold with Nonnegative Ricci Curvature
Christina Sormani
This paper concerns complete noncompact manifolds with nonnegative Ricci curvature. Roughly, we say that M has the loops to infinity property if given any noncontractible closed cu…
Harmonic Functions on Manifolds with Nonnegative Ricci Curvature and Linear Volume Growth
Christina Sormani
Lower bounds on Ricci curvature limit the volumes of sets and the existence of harmonic functions on Riemannian manifolds. In 1975, Shing Tung Yau proved that a complete noncompact…
The Almost Rigidity of Manifolds with Lower Bounds on Ricci Curvature and Minimal Volume Growth
Christina Sormani
We consider complete noncompact Riemannian manifolds with quadratically decaying lower Ricci curvature bounds and minimal volume growth. We first prove a rigidity result showing th…