Restricted families of projections and random subspaces

TL;DR

This paper investigates specific families of orthogonal projections in three-dimensional space and demonstrates that certain random subspace families satisfy a projection theorem similar to Marstrand-Mattila, advancing understanding of geometric measure theory.

Contribution

It introduces new classes of random subspaces in bcs^3 that fulfill a Marstrand-Mattila type projection theorem, extending classical results to restricted projection families.

Findings

Existence of random subspace families satisfying projection theorems

Extension of Marstrand-Mattila theorem to restricted projection families

Advancement in geometric measure theory understanding

Abstract

We study the restricted families of orthogonal projections in $\mathbb{R}^3$. We show that there are families of random subspaces which admit a Marstrand- Mattila type projection theorem.