Strong Isoperimetric Inequality for Tessellating Quantum Graphs
Metric Geometry
2018-06-27 v1 Spectral Theory
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.
Cite
@article{arxiv.1806.10096,
title = {Strong Isoperimetric Inequality for Tessellating Quantum Graphs},
author = {Noema Nicolussi},
journal= {arXiv preprint arXiv:1806.10096},
year = {2018}
}