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

Andreas Balser
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Abstract

We derive necessary conditions on the parameters of the ends of a CMC-1 trinoid in hyperbolic 3-space $H^{3}$ 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 $H^{3}$ with symmetry plane is asymptotic to a suitable helicoid.

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Andreas Balser. 2004-10-01. Towards a classification of CMC-1 Trinoids in hyperbolic space via conjugate surfaces. https://arxiv.org/abs/math/0310397

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