On the Packing Dimension and Category of Exceptional Sets of Orthogonal Projections

TL;DR

This paper explores the relationship between packing dimension and the size of exceptional sets in orthogonal projections, examining classical results and their potential reformulations, and investigates category versions of key projection theorems.

Contribution

It provides new insights into the packing dimension of exceptional sets and introduces category-based formulations of classical projection results.

Findings

Packing dimension offers a different perspective on exceptional sets.

Category versions of Marstrand and Falconer-Howroyd theorems are explored.

Results suggest possible reformulations of classical theorems in terms of category.

Abstract

We consider several classical results related to the Hausdorff dimension of exceptional sets of orthogonal projections and try to find out whether they have reasonable formulations in terms of packing dimension. We also investigate the existence of category versions for Marstrand and Falconer-Howroyd-type projection results.