2020/08/13 by Álvaro Pámpano, Alvaro Pampano
Mathematics · #Curvature #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry #Geometry and complex manifolds #Mathematical analysis #Mathematics #Mean curvature #Mean curvature flow #Pure mathematics #Scalar curvature #Space (punctuation) #Space form #Surface (topology) #Torus #Willmore energy #math.DG #msc:53C42 #msc:53C44 #msc:58E10
paper · pdf · doi:10.1016/j.na.2020.112092
published as Nonlinear Analysis 200 (2020), 112092
openalex publication_date 2020/08/13 · arxiv created 2021/09/21 · arxiv updated 2021/09/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.