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arXiv · 2411.04626

Loop Weierstrass Representation

Thomas Raujouan·Nick Schmitt·Jonas Ziefle
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Abstract

We introduce the Loop Weierstrass Representation for minimal surfaces in Euclidean space and constant mean curvature 1 surfaces in hyperbolic space by applying integral system methods to the Weierstrass and Bryant representations. We unify associated families, dual surfaces and Goursat transformations under the same holomorphic data, we introduce a simple factor dressing for minimal surfaces, and we compute and classify various examples.

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Thomas Raujouan, Nick Schmitt, Jonas Ziefle. 2024-11-07. Loop Weierstrass Representation. https://arxiv.org/abs/2411.04626

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