Absolutely minimal Lipschitz extension of tree-valued mappings

2010/05/14 by Naor, Assaf, Sheffield, Scott
#Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Metric Geometry (math.MG) #Probability (math.PR)

paper · doi:10.48550/arxiv.1005.2535

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 \citePSSW09 to study real-valued AMLEs.

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