Minimal surfaces with closed curvature lines
Differential Geometry
2026-05-12 v1
Abstract
We investigate complete non-orientable minimal surfaces of finite total curvature in such that their ends are foliated by closed lines of curvature. This condition on the ends is necessary if they have a piece inside some Euclidean ball that is free boundary. It turns out this is a rigid situation, and we are able to show, among further obstructions, that there are no such surfaces with one end.
Cite
@article{arxiv.2605.08487,
title = {Minimal surfaces with closed curvature lines},
author = {Carlos Andrés Toro Cardona},
journal= {arXiv preprint arXiv:2605.08487},
year = {2026}
}