Absolutely minimal Lipschitz extension of tree-valued mappings

Assaf Naor, Scott Sheffield

Research output: Contribution to journalArticle

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 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
Volume354
Issue number3
DOIs
StatePublished - 2012

Fingerprint

Lipschitz
Stochastic Games
Lipschitz Function
Locally Compact
Game
Metric
Subset
Generalization

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Absolutely minimal Lipschitz extension of tree-valued mappings. / Naor, Assaf; Sheffield, Scott.

In: Mathematische Annalen, Vol. 354, No. 3, 2012, p. 1049-1078.

Research output: Contribution to journalArticle

Naor, Assaf ; Sheffield, Scott. / Absolutely minimal Lipschitz extension of tree-valued mappings. In: Mathematische Annalen. 2012 ; Vol. 354, No. 3. pp. 1049-1078.
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