We prove a dimension compression estimate for homeomorphic mappings of exponentially integrable distortion via a modulus of continuity result by D. Herron and P. Koskela [Mappings of finite distortion: gauge dimension of generalized quasicircles, Illinois J. Math., 2003, 47(4), 1243–1259]. The essential sharpness of our estimate is demonstrated by an example.
We establish the basic properties of the class of generalized simply connected John domains.
We provide a geometric rigidity estimate à la Friesecke-James-Müller for conformal matrices. Namely, we replace by an arbitrary compact set of conformal matrices, bounded away from and invariant under , and rigid motions by Möbius transformations.
A classical problem in geometric topology is to recognize when a topological space is a topological manifold. This paper addresses the question of when a metric space admits a quasisymmetric parametrization by providing examples of spaces with many Eucledian-like properties which are nonetheless substantially different from Euclidean geometry. These examples are geometrically self-similar versions of classical topologically self-similar examples from geometric topology, and they can be realized...