Minimal disks bounded by three straight lines in Euclidean space and trinoids in hyperbolic space

dc.creatorDaniel, Benoit
dc.date2003-07-04
dc.date.accessioned2026-07-07T06:29:39Z
dc.date.available2026-07-07T06:29:39Z
dc.descriptionFollowing 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.description33 pages, 8 figures
dc.identifierhttps://arxiv.org/abs/math/0307066
dc.identifierhttp://arxiv.org/abs/math/0307066
dc.identifierJ. Differential Geometry 72 (3): 467-508, March 2006
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/98110
dc.subjectDifferential Geometry
dc.subject53A10; 53C42; 53A35; 30F45
dc.titleMinimal disks bounded by three straight lines in Euclidean space and trinoids in hyperbolic space
dc.typetext

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