|
|||||
|
|
|
|
|
|
|
|
|
|
|
|
|
The extremal length
systole of the cube punctured at its vertices
Samuel Dobchies and Maxime Fortier Bourque |
|
Vol. 345 (2026), No. 1, 45–84
|
 |
Abstract |
|
We prove that the extremal length systole of the cube punctured at its vertices is realized by the twelve curves surrounding its edges and give a characterization of the corresponding quadratic differentials, allowing us to estimate its value to high precision. The proof uses a mixture of exact calculations done using branched covers and elliptic integrals, together with estimates obtained using either the geometry of geodesic trajectories on the cube or explicit conformal maps. |
Keywords
extremal length, systole, punctured sphere
|
Mathematical Subject Classification
Primary: 30F30, 30F45, 31A15
|
Milestones
Received: 4 June 2024
Revised: 17 April 2026
Accepted: 9 July 2026
Published: 25 September 2026
|
Authors |
| Samuel Dobchies | |
| Département de mathématiques Université de Sherbrooke Sherbrooke Canada |
|
| Maxime Fortier Bourque | |
| Département de mathématiques et de
statistique Université de Montréal Montréal Canada |
|
| © 2026 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
Open Access made possible by participating institutions via Subscribe to Open.
