McShane-Whitney extensions for fuzzy Lipschitz maps

Extending Generalized Whitney Maps

For metrizable continua, there exists the well-known notion of a Whitney map. If X is a nonempty, compact, and metric space, then any Whitney map for any closed subset of 2X can be extended to a Whitney map for 2X [3, 16.10 Theorem]. The main purpose of this paper is to prove some generalizations of this theorem.

lipschitz groups and lipschitz maps

‎this contribution mainly focuses on some aspects of lipschitz groups‎, ‎i.e.‎, ‎metrizable groups with lipschitz multiplication and inversion map‎. ‎in the main result it is proved that metric groups‎, ‎with a translation-invariant metric‎, ‎may be characterized as particular group objects in the category of metric spaces and lipschitz maps‎. ‎moreover‎, ‎up to an adjustment of the metric‎, ‎a...

Metric Embeddings and Lipschitz Extensions

Lipschitz Maps on Trees

We introduce and study a metric notion for trees and relate it to a conjecture of Shelah [10] about the existence of a finite basis for a class of linear orderings.

Vector-valued Optimal Lipschitz Extensions

Consider a bounded open set U ⊂ Rn and a Lipschitz function g : ∂U → Rm. Does this function always have a canonical optimal Lipschitz extension to all of U? We propose a notion of optimal Lipschitz extension and address existence and uniqueness in some special cases. In the case n = m = 2, we show that smooth solutions have two phases: in one they are conformal and in the other they are variant...