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arXiv · 2608.13553

Heat kernel geometry and Gromov's volume growth conjecture

Jian Ge
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Abstract

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 entropy.

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Jian Ge. 2026-08-13. Heat kernel geometry and Gromov's volume growth conjecture. https://arxiv.org/abs/2608.13553

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