Stationary soap films with vertical potentials
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Mean curvatureElastic curveCurvature energyPhase space
Published version: Rafael López, Álvaro Pámpano, Stationary soap films with vertical potentials, Nonlinear Analysis, Volume 215, 2022, 112661, ISSN 0362-546X, [https://doi.org/10.1016/j.na.2021.112661]
SponsorshipMTM2017-89677-P, MINECO/ AEI/FEDER, UE
We classify cylindrical surfaces in the Euclidean space whose mean curvature is a nth-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.