Year: 2026
Type: preprint
Abstract: We prove that every compact connected Riemannian isometric filling $M$ of a circle of length $2π$ satisfies $\operatorname{Area}(M) \geq \frac{14ζ(3)}π \approx 5.35677$, 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 $\operatorname{Area}(M)>5.40154$.
Source: arXiv (Cornell University)
Authors: Chen, Le, Li, Xiaolong, Zhong, Yimin
Institution: Auburn University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212006202