arXiv math/03070662003-07-04math.DG

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

Benoit Daniel

备注：: 33 pages, 8 figures
发表信息：: J. Differential Geometry 72 (3): 467-508, March 2006

英文摘要：

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.

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