Noncongruent minimal surfaces with the same symmetries and conformal structure (Q1885487)

In his doctoral thesis (2000) the author, introduced certain minimal immersions of punctured compact Riemann surfaces in Euclidean three-space \(\mathbb{E}^{3}\), called ``birdcage-catenoids''. These examples of minimal surfaces illustrate that: Among complete orientable minimal surfaces in \(\mathbb{E}^{3}\) with finite total curvature and positive genus, the symmetry group and the conformal type together are still insufficient to characterize the surface.