Heat kernel geometry and Gromov's volume growth conjecture

Jian Ge

Heat kernel geometry and Gromov's volume growth conjecture

微分几何 2026-08-13 v1

作者: Jian Ge

摘要

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.

引用

@article{arxiv.2608.13553,
  title  = {Heat kernel geometry and Gromov's volume growth conjecture},
  author = {Jian Ge},
  journal= {arXiv preprint arXiv:2608.13553},
  year   = {2026}
}