Iqra Altaf

activity

20212025

collaborators

5 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.CA2023

Distance sets bounds for polyhedral norms via effective dimension

Iqra Altaf, Ryan Bushling, Bobby Wilson

We prove that, for every norm on $R^{d}$ and every $E \subseteq R^{d}$ , the Hausdorff dimension of the distance set of $E$ with respect to that norm is at least $\dim…

math.MG2022

Hausdorff dimension of Besicovitch sets of Cantor graphs

Iqra Altaf, Marianna Csörnyei, Kornélia Héra

We consider the Hausdorff dimension of planar Besicovitch sets for rectifiable sets $Γ$ , i.e. sets that contain a rotated copy of $Γ$ in each direction. We show that for a large cl…

math.CA2021

Scaled Oscillation and Level Sets

Iqra Altaf, Marianna Csornyei, Bobby Wilson

We study the size and regularity properties of level sets of continuous functions with bounded upper-scaled and lower-scaled oscillation.