PreprintThe closure of spectral data for constant mean curvature tori in \(S^3\)Emma Carberry and Martin Ulrich SchmidtAbstractThe spectral curve correspondence for finitetype solutions of the sinhGordon equation describes how they arise from and give rise to hyperelliptic curves with a real structure. Constant mean curvature (CMC) 2tori in \(S^3\) result when these spectral curves satisfy periodicity conditions. We prove that the spectral curves of CMC tori are dense in the space of smooth spectral curves of finitetype solutions of the sinhGordon equation. One consequence of this is the existence of countably many real \(n\)dimensional families of CMC tori in \(S^3\) for each positive \(n\). This paper is available as a pdf (256kB) file.
