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Absolutely minimal Lipschitz extension of tree-valued mappings

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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.

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Authors and Affiliations

  1. Courant Institute, New York University, New York, USA

    Assaf Naor

  2. Massachusetts Institute of Technology, Cambridge, USA

    Scott Sheffield

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  1. Assaf Naor
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  2. Scott Sheffield
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Correspondence to Assaf Naor.

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Naor, A., Sheffield, S. Absolutely minimal Lipschitz extension of tree-valued mappings. Math. Ann. 354, 1049–1078 (2012). https://doi.org/10.1007/s00208-011-0753-1

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