Lipschitz functions on quasiconformal trees

Grounded Lipschitz functions on trees are typically flat

A grounded M -Lipschitz function on a rooted d-ary tree is an integer-valued map on the vertices that changes by at most M along edges and attains the value zero on the leaves. We study the behavior of such functions, specifically, their typical value at the root v0 of the tree. We prove that the probability that the value of a uniformly chosen random function at v0 is more than M + t is doubly...

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.

Quasiconformal Lipschitz Maps, Sullivan's Convex Hull Theorem and Brennan's Conjecture

On fully operator Lipschitz functions

Let A(D) be the disc algebra of all continuous complex-valued functions on the unit disc D holomorphic in its interior. Functions from A(D) act on the set of all contraction operators (‖A‖ 1) on Hilbert spaces. It is proved that the following classes of functions from A(D) coincide: (1) the class of operator Lipschitz functions on the unit circle T; (2) the class of operator Lipschitz functions...

Lipschitz Functions on Topometric Spaces

We study functions on topometric spaces which are both (metrically) Lipschitz and (topologically) continuous, using them in contexts where, in classical topology, ordinary continuous functions are used. We study the relations of such functions with topometric versions of classical separation axioms, namely, normality and complete regularity, as well as with completions of topometric spaces. We ...