Characterizations of canonically compactifiable graphs via intrinsic metrics and algebraic properties
Metric Geometry
2020-09-28 v4
Abstract
We consider infinite graphs and the associated energy forms. We show that a graph is canonically compactifiable (i.e. all functions of finite energy are bounded) if and only if the underlying set is totally bounded with respect to any finite measure intrinsic metric. Furthermore, we show that a graph is canonically compactifiable if and only if the space of functions of finite energy is an algebra. These results answer questions in a recent work of Georgakopoulos, Haeseler, Keller, Lenz, Wojciechowski.
Keywords
Cite
@article{arxiv.1803.01942,
title = {Characterizations of canonically compactifiable graphs via intrinsic metrics and algebraic properties},
author = {Simon Puchert},
journal= {arXiv preprint arXiv:1803.01942},
year = {2020}
}
Comments
This is a small note solving two problems posed in "Graphs of finite measure" (arXiv:1309.3501)