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arXiv · 2605.08487

Minimal surfaces with closed curvature lines

Carlos Andrés Toro Cardona
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Abstract

We investigate complete non-orientable minimal surfaces of finite total curvature in $\mathbb{R}^3$ 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.

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Carlos Andrés Toro Cardona. 2026-05-08. Minimal surfaces with closed curvature lines. https://arxiv.org/abs/2605.08487

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