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arXiv · 1411.6100

The elastica problem under area constraint

Vincenzo Ferone·Bernd Kawohl·Carlo Nitsch
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Abstract

We show that the elastic energy $E(γ)$ of a closed curve $γ$ has a minimizer among all plane simple regular closed curves of given enclosed area $A(γ)$, and that the minimum is attained for a circle. The proof is of a geometric nature and deforms parts of $γ$ in a finite number of steps to construct some related convex sets with smaller energy.

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Vincenzo Ferone, Bernd Kawohl, Carlo Nitsch. 2015-01-10. The elastica problem under area constraint. https://arxiv.org/abs/1411.6100

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