PreprintarXiv licencearXiv
A Proof of the Area Vanishing Square Peg Conjecture
Abstract
We resolve an open problem posed by Tao related to the Toeplitz square peg conjecture. We prove that four simple closed polygonal curves in the cylinder, each winding once in the positive direction, jointly inscribe a square whenever the alternating sum of their ∫ y dx integrals vanishes. The proof reduces the problem to the non-displaceability of a pair of Lagrangian tori, which we establish using Lagrangian Floer homology.
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BibTeX
@misc{valerio2026proof,
title = {{A Proof of the Area Vanishing Square Peg Conjecture}},
author = {Lorenzo Valerio},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.21076},
eprint = {2610.21076},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.21076},
}
RIS
TY - UNPB
TI - A Proof of the Area Vanishing Square Peg Conjecture
AU - Lorenzo Valerio
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2610.21076
UR - https://arxiv.org/abs/2610.21076
AB - We resolve an open problem posed by Tao related to the Toeplitz square peg conjecture. We prove that four simple closed polygonal curves in the cylinder, each winding once in the positive direction, jointly inscribe a square whenever the alternating sum of their ∫ y dx integrals vanishes. The proof reduces the problem to the non-displaceability of a pair of Lagrangian tori, which we establish using Lagrangian Floer homology.
ER -