Author

Qing Xia

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Preprint Sep 2026

Extremal Lin--Lu--Yau Curvature: Graph Density, Girth, and Short Cycles

We develop a variational framework for extremal Lin--Lu--Yau curvature under positive edge reweighting with the combinatorial metric fixed. For a connected locally finite graph $G$, define \[ \Kmax(G) := \sup_{w>0}\inf_{e\in E(G)}\kappa_{\LLY}^w(e). \] This invariant relates edgewise discrete curvature to global combin...

Qing Xia · 0 citations

Preprint Aug 2026

Idleness Functions for Ollivier-Ricci Curvature on Hypergraphs

Let $\mathcal H=(V,E)$ be a locally finite simple hypergraph, equip $V$ with the hyperpath metric, and consider the equal-edges random walk \cite{CoupetteEtAl2023}. For adjacent vertices $x$ and $y$, we prove that the idleness function $\alpha\mapsto\kappa_\alpha^{\mathcal H}(x,y)$ is piecewise affine and with no more...

Qing Xia · 0 citations