Author

Kun-Tao Jin

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Preprint Sep 2026

Cheeger constant rigidity for cocompact negatively curved manifolds

Let $(M^m,g)$, $m\geq2$, be a closed connected Riemannian manifold with $\secg_g\leq-1$, and let $(X,g_X)$ be its universal cover. Yau proved that $\hiso(X)\geq m-1$. We prove that equality is rigid: if $\hiso(X)=m-1$, then $(X,g_X)$ is isometric to $\Hh^m(-1)$.

Kun-Tao Jin, Xiao-Dong Wang, Bo Zhu · 0 citations

Preprint Aug 2026

A sharp hyperbolic volume bound for hypersurfaces in $M^3 \times \mathbb{S}^1$

Let $(M^3, g_{\mathrm{hyp}})$ be a closed oriented hyperbolic three-manifold normalized so that $\operatorname{sec}_{g_{\mathrm{hyp}}} \equiv -1$. We prove a sharp lower bound for the volume of hypersurfaces in $M^3 \times \mathbb{S}^1$ representing the slice class $[M^3 \times \{ \mathrm{pt} \}] \in H_3(M^3 \times \ma...

Li-Zhi Chen, Kun-Tao Jin · 0 citations