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Mathematics > Metric Geometry

arXiv:2208.03818 (math)
[Submitted on 7 Aug 2022]

Title:Lipschitz means and mixers on metric spaces

Authors:Leonid V. Kovalev
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Abstract:The standard arithmetic measures of center, the mean and median, have natural topological counterparts which have been widely used in continuum theory. In the context of metric spaces it is natural to consider the Lipschitz continuous versions of the mean and median. We show that they are related to familiar concepts of the geometry of metric spaces: the bounded turning property, the existence of quasisymmetric parameterization, and others.
Subjects: Metric Geometry (math.MG)
MSC classes: Primary 51F30, Secondary 30L10, 54B20, 54C15, 54E40
Cite as: arXiv:2208.03818 [math.MG]
  (or arXiv:2208.03818v1 [math.MG] for this version)
  https://doi.org/10.48550/arXiv.2208.03818
Journal reference: Illinois J. Math., 68 (2024), no. 1, 167-187
Related DOI: https://doi.org/10.1215/00192082-11081300

Submission history

From: Leonid Kovalev [view email]
[v1] Sun, 7 Aug 2022 21:04:25 UTC (21 KB)
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