Absolutely minimal Lipschitz extension of tree-valued mappings

Assaf Naor; Scott Sheffield

doi:10.1007/s00208-011-0753-1

Absolutely minimal Lipschitz extension of tree-valued mappings

Assaf Naor
, Scott Sheffield

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

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 language	English (US)
Pages (from-to)	1049-1078
Number of pages	30
Journal	Mathematische Annalen
Volume	354
Issue number	3
DOIs	https://doi.org/10.1007/s00208-011-0753-1
State	Published - Nov 2012
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/s00208-011-0753-1

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AB - 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.

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Absolutely minimal Lipschitz extension of tree-valued mappings

Abstract

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