Bilipschitz group actions and homogeneous Jordan curves

Bilipschitz Homogeneous Curves in R2 Are Quasicircles

Doubling Property for Bilipschitz Homogeneous Geodesic Surfaces

In this paper we discuss general properties of geodesic surfaces that are (locally) biLipschitz homogeneous. In particular, we prove that they are locally doubling and there exists a special doubling measure analogous to the Haar measure for locally compact groups.

Generalized Conformal and Superconformal Group Actions and Jordan Algebras

We study the “conformal groups” of Jordan algebras along the lines suggested by Kantor. They provide a natural generalization of the concept of conformal transformations that leave 2-angles invariant to spaces where “p-angles” (p ≥ 2) can be defined. We give an oscillator realization of the generalized conformal groups of Jordan algebras and Jordan triple systems. A complete list of the general...

Homeomorphisms of Jordan Curves

The notation and terminology used in this paper are introduced in the following articles: [20], [21], [1], [3], [22], [4], [5], [19], [10], [18], [7], [17], [11], [2], [8], [9], [16], [13], [14], [15], [6], [23], and [12]. In this paper p1, p2 are points of E 2 T, C is a simple closed curve, and P is a subset of E T. Let n be a natural number, let A be a subset of En T, and let a, b be points o...

Coloring Jordan Regions and Curves

A pseudo-disk is a subset of the plane that is homeomorphic to a closed disk. Consider a family F of pseudo-disks whose interiors are pairwise disjoint, and such that any two pseudo-disks intersect in at most one point. If any point of the plane is contained in at most k elements of F (with k sufficiently large), then we show that the elements of F can be colored with at most k + 1 colors so th...