Stationary soap films with vertical potentials López Camino, Rafael Pámpano, Álvaro Mean curvature Elastic curve Curvature energy Phase space Rafael López has been partially supported by the grant no. MTM2017-89677-P, MINECO/ AEI/FEDER, UE. The authors would like to thank the referee for carefully reviewing the paper. 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. 2021-12-10T11:07:51Z 2021-12-10T11:07:51Z 2021-11-05 info:eu-repo/semantics/article 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] http://hdl.handle.net/10481/71987 eng http://creativecommons.org/licenses/by-nc-nd/3.0/es/ info:eu-repo/semantics/openAccess Atribución-NoComercial-SinDerivadas 3.0 España Elsevier