RT Journal Article
T1 Isoperimetric Inequality, p-parabolicity and Doubling Graphs
A1 Martínez Pérez, Álvaro
A1 Rodríguez, José M.
AB Herein we study the relationship on graphs between being (metric) doubling and these two properties: being p-parabolic and satisfying the Cheeger isoperimetric inequality. We prove that if a uniform graph G satisfies the (Cheeger) isoperimetric inequality, then G is not (metric) doubling and see that the converse is not true. We also prove that if G is a doubling graph with doubling constant C, then it is p-parabolic for every p ≥ log2(C) and see that the converse is not true. Furthermore, we see that being doubling does not imply being p-parabolic for every 1 <p< ∞. Finally, we see that a quasi-isometry between manifolds whose Ricci curvature is bounded below preserves being doubling and also, that an manifold with bounded Ricci curvature below is doubling if and only any uniform graph quasi-isometric to it is doubling.
PB Springer
YR 2026
FD 2026
LK https://hdl.handle.net/20.500.14352/134641
UL https://hdl.handle.net/20.500.14352/134641
LA eng
NO 2026 Acuerdos transformativos CRUE
DS Docta Complutense
RD 28 abr 2026