2010/10/15 by Hugo Jiménez-Pérez, Jiménez-Pérez, Hugo, Santiago López de Medrano +1
Mathematics · #45Q05 #53A10 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Holomorphic and Operator Theory #math.DG #msc:45Q05 #msc:53A10
paper · pdf · doi:10.48550/arxiv.1010.3049
12 pages, no figures. Restate of the principal result: mayor modifications
openalex publication_date 2010/10/15 · arxiv created 2011/12/09 · arxiv updated 2011/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Schwartz's solution to the Björling problem leads to an equivalence class of spatial strips S(t)=(c(t),n(t)) which produce equivalent minimal surfaces. For the particular case when the generating strip S(t) belongs to some plane E and c(t) is symmetric with respect to some straight line in E, the symmetries of the minimal surface permit us to identify another planar curve ~c(t) that we call the CPG curve to c(t). A simple symmetric argument shows that self-CPG curves produce minimal surfaces whose adjoint surface contains another self-CPG curve. We ask for minimal surfaces generated by self-CPG curves which are self-adjoints.