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arXiv · 1010.3049

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

Hugo Jiménez-Pérez·Santiago López de Medrano
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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.

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Hugo Jiménez-Pérez, Santiago López de Medrano. 2010-10-15. On the self-CPG curves and the Bj\"orling problem. https://arxiv.org/abs/1010.3049

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