Towards a classification of CMC-1 Trinoids in hyperbolic space via conjugate surfaces

2003/10/24 by Andreas Balser, Balser, Andreas
Mathematics · #### 53A10 ### 53C42 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53A10 #msc:53C42

paper · pdf · doi:10.48550/arxiv.math/0310397

14 pages, 1 figure; presentation improved and shortened

arxiv created 2004/10/01 · arxiv updated 2009/12/01

Abstract

We derive necessary conditions on the parameters of the ends of a CMC-1 trinoid in hyperbolic 3-space H³ with symmetry plane by passing to its conjugate minimal surface. Together with Daniel's results, this yields a classification of generic symmetric trinoids. We also discuss the relation to other classification results of trinoids by Bobenko et al. and Umehara-Yamada. To obtain the result above, we show that the conjugate minimal surface of a catenoidal CMC-1 end in H³ with symmetry plane is asymptotic to a suitable helicoid.

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