Jiayin Pan

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20242026

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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…

math.DG2024

Ricci curvature and fundamental groups of effective regular sets

Jiayin Pan

For a Gromov-Hausdorff convergent sequence of closed manifolds $M_{i}^{n} ⟶ G H X$ with $Ric \geq - (n - 1)$ , $diam (M_{i}) \leq D$ , and $\mathrm{vol}(M_i)\…