Stationary soap films with vertical potentials. (February 2022)

• Record Type: Journal Article
• Authors: López, Rafael; Pámpano, Álvaro
• Is Part Of: Nonlinear analysis. Volume 215(2022)
• Publication Date: 2022-02
• Subjects: 53C42 -- 49Q10 -- 34C05 -- 37K25; Mean curvature -- Elastic curve -- Curvature energy -- Phase space; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2021.112661
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We classify cylindrical surfaces in the Euclidean space whose mean curvature is a n th-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.