Iqra Altaf

collaborators

3 papers

math.CA2025

On the packing dimension of distance sets with respect to $C^{1}$ and polyhedral norms

Iqra Altaf, Ryan Bushling, Bobby Wilson

We prove that, for every polyhedral or $C^{1}$ norm on $R^{d}$ and every set $E \subseteq R^{d}$ of packing dimension $s$ , the packing dimension of the distance set of…

math.CA2025

On the modulus of continuity of functions whose image has positive measure, and metric embeddings into $R^{d}$ without shrinking

Iqra Altaf, Marianna Csörnyei

A generalization of the classical Sard theorem in the plane is the following. Let $f$ be a function defined on a subset $A \subset R^{2}$ . If $f$ has modulus of continuity $ω…

math.CA2024

A one-dimensional planar Besicovitch-type set

Iqra Altaf

A $Γ$ -Besicovitch set is a set which contains a rotated copy of $Γ$ in every direction. Our main result is the construction of a non-trivial $1$ -rectifiable set $Γ$ in the plane, f…

On the packing dimension of distance sets with respect to C1 and polyhedral norms

On the modulus of continuity of functions whose image has positive measure, and metric embeddings into Rd without shrinking

A one-dimensional planar Besicovitch-type set

On the packing dimension of distance sets with respect to $C^{1}$ and polyhedral norms

On the modulus of continuity of functions whose image has positive measure, and metric embeddings into $R^{d}$ without shrinking