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.

The elastica problem under area constraint

FERONE, VINCENZO;NITSCH, CARLO
2016

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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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11588/611505
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