5 citations · 8 across the 12 of their papers we have counts for
12 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…
Nonnegative Ricci Curvature and Uniformly Convex Boundary Forces Compactness
Zetian Yan, Xingyu Zhu
We confirm a compactness conjecture of M. Li. If a complete Riemannian manifold has nonnegative Ricci curvature and uniformly convex boundary in the sense that the second fundament…
Fibrations, the First Betti Number, and Almost Nonnegative Ricci Curvature
Hongzhi Huang, Xian-Tao Huang, Jikang Wang +1
In this paper, we prove fibration theorems for manifolds with almost nonnegative Ricci curvature and certain extra regularity assumptions. We show that a closed -manifold sa…
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…
Two-dimension vanishing, splitting and positive scalar curvature
Xingyu Zhu
We prove several analogs of Gromov's macroscopic dimension conjecture with extra curvature assumptions. More explicitly, we show that for an open Riemannian -manifold of…
Optimal diameter estimates of three-dimensional Ricci limit spaces
Bo Zhu, Xingyu Zhu
In this note, we prove that positive scalar curvature can pass to three dimensional Ricci limit spaces of non-negative Ricci curvature when it splits off a line. As a corollary, we…
Positive Scalar Curvature Meets Ricci Limit Spaces
Jinmin Wang, Zhizhang Xie, Bo Zhu +1
We investigate the influence of uniformly positive scalar curvature on the size of a non-collapsed Ricci limit space coming from a sequence of -manifolds with non-negative Ricci…
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…
Weakly non-collapsed RCD spaces are strongly non-collapsed
Camillo Brena, Nicola Gigli, Shouhei Honda +1
We prove that any weakly non-collapsed RCD space is actually non-collapsed, up to a renormalization of the measure. This confirms a conjecture raised by De Philippis and the second…
A characterization of non-collapsed spaces via Einstein tensors
Shouhei Honda, Xingyu Zhu
We investigate the second principal term in the expansion of metrics induced by heat kernel embedding into on a compact space. We prove that…