Strong Isoperimetric Inequality for Tessellating Quantum Graphs

2018/06/26 by Nicolussi, Noema
#34B45 #35P15 #81Q35 #FOS: Mathematics #Metric Geometry (math.MG) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1806.10096

Abstract

We investigate isoperimetric constants of infinite tessellating metric graphs. We introduce a curvature-like quantity, which plays the role of a metric graph analogue of discrete curvature notions for combinatorial tessellating graphs. We then prove a lower estimate and a criterium for positivity of the isoperimetric constant.

Related

• Sharp isoperimetric inequalities for infinite plane graphs with bounded\n vertex and face degrees
• Isoperimetric inequalities in Riemann surfaces and graphs
• Cheeger inequalities for unbounded graph Laplacians
• On torsional rigidity and ground-state energy of compact quantum graphs
• Discrete curvature and abelian groups