5 papers
Positive Scalar Curvature and Volume Growth
Bochao Kong, Xingyu Zhu
For a complete Riemannian manifold with nonnegative Ricci curvature, we prove two sharp volume growth order estimates, thereby resolve a conjecture of Gromov in 1986. There first i…
Nonnegative Ricci curvature and virtual abelianness in dimensions less than 12
Dimitri Navarro, Jiayin Pan, Xingyu Zhu
For any complete Riemannian manifold with nonnegative Ricci curvature and sublinear diameter growth, we establish a dimensional constraint if the fundament…
Complete manifolds with nonnegative Ricci curvature and slow relative volume growth
Dimitri Navarro, Jiayin Pan, Xingyu Zhu
For any complete and noncompact manifold with , we define a function that describes the growth of relative volume asymptotically $$\mathrm{R…
Topology of 3-manifolds with nonnegative scalar curvature and positive harmonic functions
Zetian Yan, Xingyu Zhu
We study complete -manifolds with nonnegative scalar curvature under additional regularity assumptions. We prove that a contractible such manifold is diffeomorphic to $\mathbb{R…
On the intrinsic and extrinsic boundary for metric measure spaces with lower curvature bounds
Vitali Kapovitch, Xingyu Zhu
We show that if an Alexandrov space has an Alexandrov subspace of the same dimension disjoint from the boundary of , then the topological boundary of coinc…