Ollivier--Ricci Curvature on Groups of Polynomial Growth

Camillo Brena; Elia Bruè

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arXiv · 2608.14232

Ollivier--Ricci Curvature on Groups of Polynomial Growth

Camillo Brena·Elia Bruè

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Abstract

We study Ollivier--Ricci curvature on Cayley graphs of groups of polynomial growth. Our main result shows that non-negative Ollivier--Ricci curvature forces the group to be virtually abelian. As an application, we prove that connected vertex-transitive graphs of polynomial growth and non-negative Ollivier--Ricci curvature are quasi-isometric to $\mathbb{Z}^k$, for some $k\in\mathbb{N}$.

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BibTeX RIS

Camillo Brena, Elia Bruè. 2026-08-14. Ollivier--Ricci Curvature on Groups of Polynomial Growth. https://arxiv.org/abs/2608.14232

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