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

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

2004-07-16

arxiv.org/abs/math/0407296v1

Mathematics

Differential Geometry

49 pages, 7 figues, PhD Thesis

Scientific paper

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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