A condition of quasiconformal extendability

A Quasiconformal Mapping?

Quasiconformalmappings are generalizations of conformalmappings. They can be considered not only on Riemann surfaces, but also on Riemannian manifolds in all dimensions, andevenon arbitrarymetric spaces. Quasiconformal mappings occur naturally in various mathematicalandoftenaprioriunrelatedcontexts. The importance of quasiconformal mappings in complex analysis was realized by Ahlfors and Teichm...

Absolute Lipschitz extendability

A metric space X is said to be absolutely Lipschitz extendable if every Lipschitz function f from X into any Banach space Z can be extended to any containing space Y ⊇ X , where the loss in the Lipschitz constant in the extension is independent of Y , Z, and f . We show that various classes of natural metric spaces are absolutely Lipschitz extendable. c © 2003 Académie des sciences/Éditions sci...

Well-covered graphs and extendability

A graph is k-extendable if every independent set of size k is contained in a maximum independent set. This generalizes the concept of a B-graph (i.e. I-extendable graph) introduced by Berge and the concept of a well-covered graph (i.e. k-extendable for every integer k) introduced by Plummer. For various graph families we present some characterizations of well-covered and k-extendable graphs. We...

Dyck path triangulations and extendability

We introduce the Dyck path triangulation of the cartesian product of two simplices ∆n−1×∆n−1. The maximal simplices of this triangulation are given by Dyck paths, and its construction naturally generalizes to produce triangulations of ∆rn−1 × ∆n−1 using rational Dyck paths. Our study of the Dyck path triangulation is motivated by extendability problems of partial triangulations of products of t...

Dynamics of Quasiconformal Fields