Critical tori for mean curvature energies in Killing submersions. (November 2020)

• Record Type: Journal Article
• Authors: Pámpano, Álvaro
• Is Part Of: Nonlinear analysis. Volume 200(2020)
• Publication Date: 2020-11
• Subjects: primary 53C42 -- secondary 58E10 53C44; BCV spaces -- Binormal evolution tori -- Closed critical curves -- Killing submersions -- Mean curvature energies -- Vertical tori; 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.2020.112092
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We study surface energies depending on the mean curvature in total spaces of Killing submersions, which extend the classical notion of Willmore energy. Based on a symmetry reduction procedure, we construct vertical tori critical for these mean curvature energies. These vertical tori are based on closed curves critical for curvature energy functionals in Riemannian 2-space forms. The binormal evolution of these critical curves in Riemannian 3-space forms generates rotational tori solutions for an ample family of Weingarten surfaces. Therefore, we also introduce some correspondence results between these two types of tori and illustrate their relation.