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A Fourier approach to Gromov's filling area conjecture
Abstract
We prove that every compact connected Riemannian isometric filling M of a circle of length 2π satisfies Area(M) ≥ 14ζ(3)/π ≈ 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 Area(M)>5.40154.
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BibTeX
@misc{chen2026fourier,
title = {{A Fourier approach to Gromov's filling area conjecture}},
author = {Le Chen and Xiaolong Li and Yimin Zhong},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.08251},
eprint = {2609.08251},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.08251},
}
RIS
TY - UNPB
TI - A Fourier approach to Gromov's filling area conjecture
AU - Le Chen
AU - Xiaolong Li
AU - Yimin Zhong
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.08251
UR - https://arxiv.org/abs/2609.08251
AB - We prove that every compact connected Riemannian isometric filling M of a circle of length 2π satisfies Area(M) ≥ 14ζ(3)/π ≈ 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 Area(M)>5.40154.
ER -