Jiayin Pan

activity

20242026

collaborators

5 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

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

Universal non-CD of sub-Riemannian manifolds

Dimitri Navarro, Jiayin Pan

We prove that a sub-Riemannian manifold equipped with a full-support Radon measure is never $CD (K, N)$ for any $K \in R$ and $N \in (1, \infty)$ unless it is Riemanni…

math.DG2025

Nonnegative Ricci curvature, nilpotency, and Hausdorff dimension

Jiayin Pan

Let $M$ be an open (complete and non-compact) manifold with $Ric \geq 0$ and escape rate not $1/2$ . It is known that under these conditions, the fundamental group $I ¨ _{1} (M)$ …

math.DG2024

On the topology of manifolds with nonnegative Ricci curvature and linear volume growth

Dimitri Navarro, Jiayin Pan, Xingyu Zhu

Understanding the relationships between geometry and topology is a central theme in Riemannian geometry. We establish two results on the fundamental groups of open (complete and no…