Absolutely minimal Lipschitz extension of tree-valued mappings
Metric Geometry
2010-05-17 v1 Analysis of PDEs
Functional Analysis
Probability
Abstract
We prove that every Lipschitz function from a subset of a locally compact length space to a metric tree has a unique absolutely minimal Lipschitz extension (AMLE). We relate these extensions to a stochastic game called {\bf Politics} - a generalization of a game called {\bf Tug of War} that has been used in \cite{PSSW09} to study real-valued AMLEs.
Keywords
Cite
@article{arxiv.1005.2535,
title = {Absolutely minimal Lipschitz extension of tree-valued mappings},
author = {Assaf Naor and Scott Sheffield},
journal= {arXiv preprint arXiv:1005.2535},
year = {2010}
}