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math.DG2026
Structure theorems for Lichnerowicz-sharp graphs
Yanlong Ding, Shiping Liu, Chiyu Zhou
Hypercube graphs are fundamental model spaces of positive curvature in discrete comparison geometry. Let be a finite, connected, simple, unweighted graph with Bakry--Émery curv…
math.DG2026
Equivalence of Lin--Lu--Yau curvature and 1/2-Ollivier curvature on weighted graphs
Shiping Liu, Yunyan Yang
In this note, we prove that, on weighted graphs, the Lin--Lu--Yau curvature coincides with the -Ollivier curvature up to scaling whenever the idleness parameter . Mor…
math.DG2026
Regular Lichnerowicz-sharp graphs are hypercube bundles
Yanlong Ding, Shiping Liu, Chiyu Zhou
Hypercube graphs are fundamental model spaces of positive curvature in discrete comparison geometry. Let be a finite, connected, simple, unweighted graph with Bakry--Émery curv…