Exceptional sets of projections, unions of k-planes, and associated transforms

TL;DR

This paper generalizes a result on the dimensions of exceptional projection sets and applies it to a geometric problem involving unions of k-planes, advancing understanding of projection behavior in geometric measure theory.

Contribution

It extends previous work by Peres and Schlag on projection dimensions and introduces new applications to unions of k-planes.

Findings

Generalized the dimension estimates for exceptional projection sets

Applied the results to unions of k-planes in geometric problems

Provided new insights into associated transforms and their behavior

Abstract

We prove a generalization of a result of Peres and Schlag on the dimensions of certain exceptional sets of projections and then apply it to a geometric problem.