Absolutely minimal Lipschitz extension of tree-valued mappings |
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| Authors: | Assaf Naor Scott Sheffield |
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| Affiliation: | 1. Courant Institute, New York University, New York, USA
2. Massachusetts Institute of Technology, Cambridge, USA
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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?C210, 2009) to study real-valued AMLEs. |
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