28 citations · 60 across the 15 of their papers we have counts for
19 papers
On uniform measures in the Heisenberg group
Vasilis Chousionis, Valentino Magnani, Jeremy T. Tyson
We initiate a classification of uniform measures in the first Heisenberg group equipped with the Korányi metric , that represents the first example of a noncommuta…
The Traveling Salesman Theorem in Carnot Groups
Vasileios Chousionis, Sean Li, Scott Zimmerman
Let be any Carnot group. We prove that, if a subset of is contained in a rectifiable curve, then it satisfies Peter Jones' geometric lemma with some natur…
Conformal graph directed Markov systems on Carnot groups
Vasilis Chousionis, Jeremy T. Tyson, Mariusz Urbański
We develop a comprehensive theory of conformal graph directed Markov systems in the non-Riemannian setting of Carnot groups equipped with a sub-Riemannian metric. In particular, we…
Marstrand's density theorem in the Heisenberg group
Vasilis Chousionis, Jeremy T. Tyson
We prove that if is a Radon measure on the Heisenberg group such that the density , computed with respect to the Korányi metric , exists and i…
Fractal solutions of linear and nonlinear dispersive partial differential equations
V. Chousionis, M. Burak Erdoğan, Nikolaos Tzirakis
In this paper we study fractal solutions of linear and nonlinear dispersive PDE on the torus. In the first part we answer some open questions on the fractal solutions of linear Sch…
Some Calderón-Zygmund kernels and their relations to Wolff capacities and rectifiability
Vasilis Chousionis, Laura Prat
We consider the Calderón-Zygmund kernels in for and . We show that, on the plane, for $0<…