arXiv subjects

Hervé Pajot

Publications and source records attributed to Hervé Pajot.

3 recordsLinked to original sources

arXiv2026

Edge-regular graphs with non-negative curvature have polynomial growth

A long-standing conjecture in the emerging discrete Bakry-Émery theory asserts that bounded-degree graphs satisfying $\mathrm{CD}(0,\infty)$ have polynomial growth. In the present paper, we prove this conjecture for all edge-regular graphs, and even obtain a volume doubling estimate with a constant that depends only on the degree. This is made possible thanks to the discovery of a surprising self-improvement phenomenon, which seems of independent interest: any edge-regular graph satisfying $\mathrm{CD}(κ,\infty)$ for some $κ\in\mathbb R$ must in fact satisfy $\mathrm{CD}(κ,n)$ for some explicit, universal and optimal dimension parameter $n$.

math.CO↗

arXiv2025

Infinite graphs satisfying the Bakry-Emery curvature condition CD(0, n): The modified heat equation and applications to geometric analysis

Let G = (V, p, $μ$) be a (finite or infinite) weighted graph with bounded geometry. Assuming that G satisfies the classical curvaturedimension condition of Bakry-Emery CD(K, n) with K $\ge$ 0 (for the usual Laplacian), we prove that the doubling volume property holds. One of the key points is to establish the existence and uniqueness of solutions of a modified non linear heat equation which replaces the standard one usually used in the case of Riemannian manifolds. Li-Yau and Harnack estimates for the solutions of this modified heat equation are obtained. We also provide explicit examples of Cayley graphs satisfying our assumptions.

math.DG↗

arXiv1997

Poincaré inequalities and quasiconformal structure on the boundary of some hyperbolic buildings

In this paper we shall show that the boundary $\partial I_{p,q}$ of the hyperbolic building $I_{p,q}$ considered in M. Bourdon, \emph{Immeubles hyperboliques, dimension conforme et rigidité de Mostow} (Geometric And Functional Analysis, Vol 7 (1997), p 245-268) admits Poincaré type inequalities. Then by using Heinonen-Koskela's work, we shall prove Loewner capacity estimates for some families of curves of $\partial I_{p,q}$ and the fact that every quasiconformal homeomorphism $f : \partial I_{p,q} \longrightarrow \partial I_{p,q}$ is quasisymetric. Therefore by these results, the answers to certain questions of Heinonen and Semmes are NO.

math.DG↗