Absolutely minimal Lipschitz extension of tree-valued mappings

Author(s)
Naor, Assaf; Sheffield, Scott Roger
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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.
Date issued
2011-11
URI
http://hdl.handle.net/1721.1/80844
Department
Massachusetts Institute of Technology. Department of Mathematics
Journal
Mathematische Annalen
Publisher
Springer-Verlag
Citation
Naor, Assaf, and Scott Sheffield. “Absolutely minimal Lipschitz extension of tree-valued mappings.” Mathematische Annalen 354, no. 3 (November 15, 2012): 1049-1078.
Version: Original manuscript
ISSN
0025-5831
1432-1807
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