Absolutely minimal Lipschitz extension of tree-valued mappings

Assaf Naor, Scott Sheffield

Research output: Contribution to journalArticlepeer-review


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 Peres et al. (J Am Math Soc 22(1):167-210, 2009) to study real-valued AMLEs.

Original languageEnglish (US)
Pages (from-to)1049-1078
Number of pages30
JournalMathematische Annalen
Issue number3
StatePublished - Nov 2012

ASJC Scopus subject areas

  • General Mathematics


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