Minimal disks bounded by three straight lines in Euclidean space and trinoids in hyperbolic space
| dc.creator | Daniel, Benoit | |
| dc.date | 2003-07-04 | |
| dc.date.accessioned | 2026-07-07T06:29:39Z | |
| dc.date.available | 2026-07-07T06:29:39Z | |
| dc.description | Following Riemann's idea, we prove the existence of a minimal disk in Euclidean space bounded by three lines in generic position and with three helicoidal ends of angles less than $π$. In the case of general angles, we prove that there exist at most four such minimal disks, we give a sufficient condition of existence in terms of a system of three equations of degree 2, and we give explicit formulas for the Weierstrass data in terms of hypergeometric functions. Finally, we construct constant-mean-curvature-one trinoids in hyperbolic space by the method of the conjugate cousin immersion. | |
| dc.description | 33 pages, 8 figures | |
| dc.identifier | https://arxiv.org/abs/math/0307066 | |
| dc.identifier | http://arxiv.org/abs/math/0307066 | |
| dc.identifier | J. Differential Geometry 72 (3): 467-508, March 2006 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/98110 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53A10; 53C42; 53A35; 30F45 | |
| dc.title | Minimal disks bounded by three straight lines in Euclidean space and trinoids in hyperbolic space | |
| dc.type | text |