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