TY - JOUR
T1 - Lipschitz means and mixers on metric spaces
AU - Kovalev, Leonid V.
N1 - Publisher Copyright:
© 2024 by the University of Illinois Urbana-Champaign.
PY - 2024/4
Y1 - 2024/4
N2 - The standard arithmetic measures of center, the mean, and the median, have natural topological counterparts that 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.
AB - The standard arithmetic measures of center, the mean, and the median, have natural topological counterparts that 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.
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U2 - 10.1215/00192082-11081300
DO - 10.1215/00192082-11081300
M3 - Article
AN - SCOPUS:85188548810
SN - 0019-2082
VL - 68
SP - 167
EP - 187
JO - Illinois Journal of Mathematics
JF - Illinois Journal of Mathematics
IS - 1
ER -