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On nearly optimal paper Moebius bands

  • Richard Evan Schwartz
Published/Copyright: May 15, 2025
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Abstract

Let ε < 1/324 and let Ω be a smooth embedded paper Moebius band of aspect ratio less than 3+ε. We prove that Ω is within Hausdorff distance 18ε of an equilateral triangle of perimeter 23. This is an effective and fairly sharp version of our recent theorems in [6] about the optimal paper Moebius band.

MSC 2010: 53A05

Funding statement: This research is supported by a Simons Sabbatical Fellowship, a grant from the National Science Foundation (N.S.F. Grant DMS-2102802), and a Mercator Fellowship. I’d like to thank all these organizations.

Acknowledgements

In [6] I thanked many people for their help and insights into paper Moebius bands. I thank all these people again.

  1. Communicated by: R. Löwen

References

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Received: 2024-11-22
Published Online: 2025-05-15
Published in Print: 2025-04-28

© 2025 Walter de Gruyter GmbH, Berlin/Boston

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