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Abstract
In this paper we prove that a smooth embedded paper Moebius band must have aspect ratio greater than $\sqrt 3$. We also prove that any sequence of smooth embedded paper Moebius bands whose aspect ratio converges to $\sqrt 3$ must converge, up to isometry, to the famous triangular Moebius band. These results answer the minimum aspect ratio question discussed by W. Wunderlich in 1962 and prove the more specific conjecture of B Halpern and C. Weaver from 1977.
arXiv comments
This paper has been accepted for publication by the Annals of Mathematics. This is the final version, the one I am publishing. This differs from the previous version in two ways: I removed an appendix and I changed the typesetting to the journal's specs
Linked by 1 identifiable commenter in 1 comment across 1 thread, from Jul 2024 to Jul 2024. Found in 1 HN submission from Oct 2023 to Oct 2023. Open submission discussions.
Original paper https://arxiv.org/pdf/2308.12641
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