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Analysis shows pairs of non-isometric free boundary minimal surfaces exist, indicating topology alone doesn't determine uniqueness.
The topology and symmetry group of a free boundary minimal surface in the three-dimensional Euclidean unit ball do not determine the surface uniquely. We provide pairs of non-isometric free boundary minimal surfaces having any sufficiently large genus g g , three boundary components and antiprismatic symmetry group of order 4 ( g + 1 ) 4(g+1) .
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Carlotto et al. (2025) studied this question.
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