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.
All Science Journal Classification (ASJC) codes
- General Mathematics