English

On the self-CPG curves and the Bj\"orling problem

Differential Geometry 2011-12-12 v4

Abstract

Schwartz's solution to the Bj\"orling 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.

Keywords

Cite

@article{arxiv.1010.3049,
  title  = {On the self-CPG curves and the Bj\"orling problem},
  author = {Hugo Jiménez-Pérez and Santiago López de Medrano},
  journal= {arXiv preprint arXiv:1010.3049},
  year   = {2011}
}

Comments

12 pages, no figures. Restate of the principal result: mayor modifications

R2 v1 2026-06-21T16:28:46.916Z