Ryan E. G. Bushling

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math.CA2025

Strong exceptional parameters for the dimension of nonlinear slices

Ryan E. G. Bushling

Let $1 \leq m < s \leq n$ and let $A \subseteq R^{n}$ be a Borel set of with $s$ -dimensional Hausdorff measure $H^{s} (A) > 0$ . The classical Marstrand slicing theore…

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

Bounds on the dimension of lineal extensions

Ryan E. G. Bushling, Jacob B. Fiedler

Let $E \subseteq R^{n}$ be a union of line segments and $F \subseteq R^{n}$ the set obtained from $E$ by extending each line segment in $E$ to a full line. Keleti's l…

math.CA2024

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.CA2024

Exceptional projections of sets exhibiting almost dimension conservation

Ryan E. G. Bushling

We establish a packing dimension estimate on the exceptional sets of orthogonal projections of sets satisfying an almost dimension conservation law. In particular, the main result…

Strong exceptional parameters for the dimension of nonlinear slices

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

Bounds on the dimension of lineal extensions

Distance sets bounds for polyhedral norms via effective dimension

Exceptional projections of sets exhibiting almost dimension conservation

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