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On the Existence of Minimal Tori in $S^3$ of Arbitrary Spectral Genus

Emma Carberry
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Abstract

Minimal tori that are linearly full in the 3-sphere possess a natural invariant g called their spectral genus, which was introduced by Hitchin. We show that for each g>0, there are countably many real g-dimensional families of minimally immersed tori with spectral genus g (two of these dimensions are just reparametrisations of the torus). Each family maps from a fixed torus of rectangular conformal type.

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Emma Carberry. 2004-07-16. On the Existence of Minimal Tori in $S^3$ of Arbitrary Spectral Genus. https://arxiv.org/abs/math/0407296

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