46. chen.li.ea:26:fourier#
A Fourier approach to Gromov’s filling area conjecture
Le Chen, Xiaolong Li and Yimin Zhong
Abstract: We prove that every compact connected Riemannian isometric filling \(M\) of a circle of length \(2\pi\) satisfies
\[\operatorname{Area}(M) \geq \frac{14\zeta(3)}{\pi} \approx 5.35677,\]
regardless of orientability or topological types. Our new approach uses the odd Fourier coefficients of the distance functions from boundary points. For orientable fillings, we use a cubic resonant perturbation to obtain \(\operatorname{Area}(M) > 5.40154\).
Lean formalization: GitHub repository, documentation site
[CLZ26] Le Chen, Xiaolong Li & Yimin Zhong (2026) ‘A Fourier approach to Gromov’s filling area conjecture’, preprint arXiv:2609.08251, 20 pages
@article{chen.li.ea:26:fourier,
title = {A Fourier approach to {G}romov's filling area conjecture},
author = {Le Chen and Xiaolong Li and Yimin Zhong},
year = {2026},
month = {September},
journal = {Preprint arXiv:2609.08251},
url = {http://arXiv.org/abs/2609.08251}
}