Exceptional projections of sets exhibiting almost dimension conservation

TL;DR

This paper provides a packing dimension estimate for the exceptional sets of orthogonal projections of sets that nearly preserve their dimension, with applications to homogeneous and graph-directed sets.

Contribution

It introduces a new packing dimension estimate for projections of sets satisfying an almost dimension conservation law, extending previous results to broader classes.

Findings

Packing dimension estimate for exceptional projection sets

Application to homogeneous and graph-directed sets

Connections to prior work by Rams and Orponen

Abstract

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 applies to homogeneous sets and to certain graph-directed sets. Connections are drawn to results of M. Rams and T. Orponen.