4 papers · 1 filter
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…
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…