Continuity of extensions of Lipschitz maps

We establish the sharp rate of continuity of extensions of ℝm-valued 1-Lipschitz maps from a subset A of ℝn to a 1-Lipschitz maps on ℝn. We consider several cases when there exists a 1-Lipschitz extension with preserved uniform distance to a given 1-Lipschitz map. We prove that if m > 1, then a g...