10 papers
A purely metric characterization of supercritical Sobolev spaces
Ryan Alvarado, Efstathios Konstantinos Chrontsios Garitsis
In this paper we provide a purely metric and derivative-free characterization of continuous mappings in the local supercritical Sobolev space. More specifically, we show that a con…
On the Assouad dimension of Weierstrass function graphs
Efstathios Konstantinos Chrontsios Garitsis
The class of Weierstrass functions is one of the first class of examples of continuous and nowhere differentiable real functions. A challenging line of research has been…
Sobolev spaces on snowtrees
Efstathios Konstantinos Chrontsios Garitsis, Vyron Vellis
We introduce a discrete-energy Sobolev space on Ahlfors regular snowtrees, a class of metric trees where every arc is a snowflake of the same ty…
Hölder spiral arcs
Efstathios Konstantinos Chrontsios Garitsis, Vyron Vellis
We establish a quantitative necessary and sufficient condition for a spiral arc to be a Hölder arc. The class of spiral arcs contains the polynomial spirals studied by Fraser, and…
Dimensions and metric dyadic cubes
Efstathios Konstantinos Chrontsios Garitsis
In this note, we provide equivalent definitions for fractal geometric dimensions through dyadic cube constructions. Given a metric space with finite Assouad dimension, i.e., sa…
Universal quasiconformal trees
Efstathios Konstantinos Chrontsios Garitsis, Fotis Ioannidis, Vyron Vellis
A quasiconformal tree is a doubling (compact) metric tree in which the diameter of each arc is comparable to the distance of its endpoints. We show that for each integer ,…
Minkowski weak embedding theorem
Efstathios Konstantinos Chrontsios Garitsis, Sascha Troscheit
A well-known theorem of Assouad states that metric spaces satisfying the doubling property can be snowflaked and bi-Lipschitz embedded into Euclidean spaces. Due to the invariance…
Sobolev mappings on metric spaces and Minkowski dimension
Efstathios Konstantinos Chrontsios Garitsis
We introduce the class of compactly Hölder mappings between metric spaces and determine the extent to which they distort the Minkowski dimension of a given set. These mappings are…
Quasiregular distortion of dimensions
Efstathios Konstantinos Chrontsios Garitsis
We investigate the distortion of the Assouad dimension and (regularized) spectrum of sets under planar quasiregular maps. While the respective results for the Hausdorff and upper b…
A geometric property of quadrilaterals
Efstathios Konstantinos Chrontsios Garitsis, Aimo Hinkkanen
Quadrilaterals in the complex plane play a significant part in the theory of planar quasiconformal mappings. Motivated by the geometric definition of quasiconformality, we prove th…