The rectifiable rectangular peg problem

TL;DR

This paper proves the rectangular peg problem for a broad class of continuous Jordan curves, including rectifiable and locally monotone curves, using advanced microlocal sheaf theory techniques.

Contribution

It introduces a novel proof approach for the rectangular peg problem applicable to a large class of curves, expanding previous results.

Findings

Confirmed the rectangular peg problem for rectifiable and Stromquist's locally monotone curves.

Utilized microlocal sheaf theory in geometric problem-solving.

Extended the class of curves for which the problem is solved.

Abstract

We give an affirmative answer to the rectangular peg problem for a large class of continuous Jordan curves that contains all rectifiable curves and Stromquist's locally monotone curves. Our proof is based on microlocal sheaf theory and inspired by recent work of Greene and Lobb.