English

The rectifiable rectangular peg problem

Symplectic Geometry 2026-01-06 v3 Geometric Topology Metric Geometry

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.

Keywords

Cite

@article{arxiv.2412.21057,
  title  = {The rectifiable rectangular peg problem},
  author = {Tomohiro Asano and Yuichi Ike},
  journal= {arXiv preprint arXiv:2412.21057},
  year   = {2026}
}

Comments

30 pages, v3:Revised. v2:An error in Section 5 fixed. Many typos fixed