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arXiv · 2204.01096

Closed 1/2-Elasticae in the 2-Sphere

Emilio Musso·Alvaro Pampano
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Abstract

We study critical trajectories in the sphere for the $1/2$-Bernoulli's bending functional with length constraint. For every Lagrange multiplier encoding the conservation of the length during the variation, we show the existence of infinitely many closed trajectories which depend on a pair of relatively prime natural numbers. A geometric description of these numbers and the relation with the shape of the corresponding critical trajectories is also given.

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Emilio Musso, Alvaro Pampano. 2022-04-03. Closed 1/2-Elasticae in the 2-Sphere. https://arxiv.org/abs/2204.01096

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