Year: 2026
Type: preprint
Abstract: We construct explicit area-minimizing polyhedral disks in $\R^n$ with the maximum norm for $n=2,3,4$. Their boundaries are polygonal images of the geodesic circle of length $2π$, obtained from $n$ distance functions. Piecewise constant calibrations show that these disks minimize mass among Ambrosio--Kirchheim metric currents with the same boundary. The example for $n=4$ gives the lower bound $11π^2/20\approx5.42828$ for Gromov's filling area conjecture. For $n>4$, finite linear programs provide further lower bounds.
Source: arXiv (Cornell University)
Author: Züst, Roger
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223200093