English

Loop Weierstrass Representation

Differential Geometry 2024-11-08 v1

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.

Keywords

Cite

@article{arxiv.2411.04626,
  title  = {Loop Weierstrass Representation},
  author = {Thomas Raujouan and Nick Schmitt and Jonas Ziefle},
  journal= {arXiv preprint arXiv:2411.04626},
  year   = {2024}
}

Comments

33 pages, 5 figures