Absolutely minimal Lipschitz extension of tree-valued mappings
Name
Sheffield_Absolutely minimal.pdf
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361.4 KB
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Checksum (MD5)
71fffa2d7cd318c7f95605e02d2e620a
Author(s)
Naor, Assaf
Sheffield, Scott Roger
Date Issued
November 2011
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
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike 3.0
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DOI of Published Version
https://doi.org/10.1007/s00208-011-0753-1
