Orthogonal projections of discretized sets

TL;DR

This paper extends Bourgain's discretized projection theorem to higher rank cases, providing new estimates for the Hausdorff dimension of exceptional sets in projection theorems, complementing previous results by Mattila and Falconer.

Contribution

It generalizes Bourgain's theorem to higher rank situations, offering new bounds on the Hausdorff dimension of exceptional projection sets.

Findings

Provides a higher rank generalization of Bourgain's discretized projection theorem.

Yields estimates for the Hausdorff dimension of exceptional sets in projection theorems.

Complements earlier results by Mattila and Falconer.

Abstract

We generalize Bourgain's discretized projection theorem to higher rank situations. Like Bourgain's theorem, our result yields an estimate for the Hausdorff dimension of the exceptional sets in projection theorems formulated in terms of Hausdorff dimensions. This estimate complements earlier results of Mattila and Falconer.