HEXAGONbeta

A LOWER BOUND FOR THE FILLING AREA OF THE CIRCLE

Primarily AI-generated textHuman understanding: no partsmath.DG — Differential Geometrymath.MG — Metric Geometry

Contributed by Qiyue Tang ↗

Version 1 / Nov 10, 2026 / CC BY 4.0

Abstract

We establish a universal lower bound for the area of orientable Riemannian fillings of the circle.

Provenance statement

Recently, our team has been exploring AI’s capabilities in the field of metric geometry. This question is a test. Uploading this paper to this platform does not mean that I claim ownership or copyright over it. My sole intention is to share this AI-generated solution and make it available for independent review. Once its correctness has been independently verified, the paper may be cited directly. GPT-6-Pro was used in two main research runs, with durations of approximately 2 and 5.5 hours, respectively (approximately 7.5 hours in total). GPT-6-Pro was also used for mathematical review, verification assistance, and manuscript editing. A revised version with more readable exposition and an additional audit by Rethlas-OSV will be added later.

References

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  2. J. Briggs and C. Wells, A discrete view of Gromov's filling area conjecture , preprint (2026), arXiv:2602.17859v1 (https://arxiv.org/abs/2602.17859v1).arXiv
  3. L. Chen, X. Li and Y. Zhong, A Fourier approach to Gromov's filling area conjecture , preprint (2026), arXiv:2609.08251v1 (https://arxiv.org/abs/2609.08251v1).arXiv
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  5. S. Ivanov, Filling minimality of Finslerian 22-discs , Proc. Steklov Inst. Math. 273 (2011), 176--190. doi:10.1134/S0081543811040079 (https://doi.org/10.1134/S0081543811040079).DOI
  6. R. Züst, Examples of absolutely minimal polyhedral chains in maximum norm spaces , preprint (2026), arXiv:2610.29593v1 (https://arxiv.org/abs/2610.29593v1).arXiv

Version history

  1. v1 · 15 pagesSubmitted by Qiyue TangInitial depositCurrentNov 08, 2026