Author

Jian-Quan Ge

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Preprint Aug 2026

Heat kernel geometry and Gromov's volume growth conjecture

In 1986, Gromov asked whether every complete noncompact $n$-dimensional Riemannian manifold with nonnegative Ricci curvature and scalar curvature at least one satisfies: \[ \Vol_g (B(p, R))\le C_{n}R^{n-2} \] for all $p\in M$ and $R>0$. We answer this question affirmatively using the heat-kernel Fisher metric and Nash...

Jian-Quan Ge · 3 citations · ⚡1

Preprint Sep 2026

The Second Gap and Rigidity in Chern's Conjecture with Constant Cubic Trace

Let $M^n\subset\mathbb{S}^{n+1}(1)$ be a closed minimal hypersurface with constant $S=|h|^2$ and constant $f_3=\operatorname{tr} h^3$, where $h$ is the shape operator. We prove that $S>n$ implies $S\geq2n$, and that the equality images are precisely the minimal Cartan isoparametric hypersurfaces with three principal cu...

Jian-Quan Ge, Hui-Xin Tan, Wen-Jiao Yan et al. · 3 citations