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arXiv · 2111.03293

Stationary soap films with vertical potentials

Rafael López·Alvaro Pámpano
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Abstract

We classify cylindrical surfaces in the Euclidean space whose mean curvature is a $n$th-power of the distance to a reference plane. The generating curves of these surfaces, called $n$-elastic curves, have a variational characterization as critical points of a curvature energy generalizing the classical elastic energy. We give a full description of such curves obtaining, in some particular cases, closed curves including simple ones.

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Rafael López, Alvaro Pámpano. 2021-11-05. Stationary soap films with vertical potentials. https://arxiv.org/abs/2111.03293

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