Plenty of big projections imply big pieces of Lipschitz graphs

TL;DR

The paper proves that certain regular sets with large projections contain significant portions that are Lipschitz graphs, addressing a question posed by David and Semmes.

Contribution

It establishes a new link between large projections and the existence of Lipschitz graph pieces in regular sets, advancing geometric measure theory.

Findings

Sets with big projections have big Lipschitz graph pieces.

Addresses a longstanding question by David and Semmes.

Enhances understanding of geometric structure of regular sets.

Abstract

I prove that a closed $n$-regular set $E \subset \mathbb{R}^{d}$ with plenty of big projections has big pieces of Lipschitz graphs. This answers a question of David and Semmes.