Infinity modulus and the essential metric

We study ∞-modulus on general metric spaces and establish its relation to lengths of paths. This connection was already known for modulus on graphs, but the formulation in metric measure spaces requires more attention to exceptional families. We use this to define a metric that we call the essential...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2018-11, Vol.467 (1), p.570-584
Main Authors: Albin, Nathan, Hoppis, Jared, Poggi-Corradini, Pietro, Shanmugalingam, Nageswari
Format: Article
Language:English
Subjects:
Essential distance
Infinity modulus
Metric measure spaces
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Summary:We study ∞-modulus on general metric spaces and establish its relation to lengths of paths. This connection was already known for modulus on graphs, but the formulation in metric measure spaces requires more attention to exceptional families. We use this to define a metric that we call the essential metric, and show how this recovers a metric that had already been advanced in the literature by De Cecco and Palmieri.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2018.07.028