First embedded compact special Legendrian surfaces in S^5 of genus >1 are constructed for Fermat curves of sufficiently large degree k.
Traizet,Construction of constant mean curvaturen-noids using the DPW method, J
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Embedded special Legendrian surfaces in $\mathbb S^5$
First embedded compact special Legendrian surfaces in S^5 of genus >1 are constructed for Fermat curves of sufficiently large degree k.