Xingyu Zhu

collaborators

7 papers

math.DG2026

Nonnegative Ricci curvature and virtual abelianness in dimensions less than 12

Dimitri Navarro, Jiayin Pan, Xingyu Zhu

For any complete Riemannian manifold $M^{n}$ with nonnegative Ricci curvature and sublinear diameter growth, we establish a dimensional constraint $n \geq 4 s (s - 1) + k + 1$ if the fundament…

math.DG2026

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…

math.DG2026

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 $n$ -manifold $M$ sa…

math.DG2026

Complete manifolds with nonnegative Ricci curvature and slow relative volume growth

Dimitri Navarro, Jiayin Pan, Xingyu Zhu

For any complete and noncompact manifold $M$ with $Ric \geq 0$ , we define a function $RV (s)$ that describes the growth of relative volume asymptotically $$\mathrm{R…

math.DG2026

Topology of 3-manifolds with nonnegative scalar curvature and positive harmonic functions

Zetian Yan, Xingyu Zhu

We study complete $3$ -manifolds with nonnegative scalar curvature under additional regularity assumptions. We prove that a contractible such manifold is diffeomorphic to $\mathbb{R…

math.DG2024

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 $n$ -manifold $(M, g)$ of…