# Universal Mappings and Analysis of Functional Data on Geometric Domains

@inproceedings{Anbouhi2022UniversalMA, title={Universal Mappings and Analysis of Functional Data on Geometric Domains}, author={Soheil Anbouhi and Washington Mio and Osman Berat Okutan}, year={2022} }

This paper employs techniques from metric geometry and optimal transport theory to address questions related to the analysis of functional data on metric or metric-measure spaces, which we refer to as ﬁelds. Formally, ﬁelds are viewed as 1-Lipschitz mappings between Polish spaces, with the domain possibly equipped with a probability measure. We establish the existence and uniqueness, up to isometry, of Urysohn ﬁelds; that is, universal and homogeneous elements for this class. We prove a…

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