Absolutely minimal Lipschitz extension of tree-valued mappings
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 Politics - a generalization of a game called Tug of War that has been used in PSSW09 to study real-valued AMLEs.
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