Minimal immersions of surfaces by the first eigenfunctions and conformal area
The authors study compact minimal surfaces immersed in a unit sphere for which 2 is the first eigenvalue of the Laplacian (or equivalently, the immersion is given by the first eigenfunctions). The main results are as follows: (1) For each conformal structure on a compact surface, there exists at most one metric which admits a minimal immersion into some unit sphere by the first eigenfunctions. (2) The only minimal torus immersed into \(S^ 3\) by the first eigenfunctions is the Clifford torus. (3) There exist conformal structures on a torus for which there are no metrics admitting minimal immersions into any sphere by the first eigenfunctions.
scientific article; zbMATH DE number 3935902