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

Mathematics

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

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

ASJC Scopus subject areas

Mathematics(all)

Access to Document

10.1007/s00208-011-0753-1

Cite this

@article{ff4811ec9c274dc59649c79ff4494365,

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

author = "Assaf Naor and Scott Sheffield",

year = "2012",

month = nov,

doi = "10.1007/s00208-011-0753-1",

language = "English (US)",

volume = "354",

pages = "1049--1078",

journal = "Mathematische Annalen",

issn = "0025-5831",

publisher = "Springer New York",

number = "3",

}

TY - JOUR

T1 - Absolutely minimal Lipschitz extension of tree-valued mappings

AU - Naor, Assaf

AU - Sheffield, Scott

PY - 2012/11

Y1 - 2012/11

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=84867521689&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84867521689&partnerID=8YFLogxK

U2 - 10.1007/s00208-011-0753-1

DO - 10.1007/s00208-011-0753-1

M3 - Article

AN - SCOPUS:84867521689

SN - 0025-5831

VL - 354

SP - 1049

EP - 1078

JO - Mathematische Annalen

JF - Mathematische Annalen

IS - 3

ER -

Absolutely minimal Lipschitz extension of tree-valued mappings

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this