Embedded special Legendrian surfaces in $\mathbb S^5$
Differential Geometry
2026-04-24 v1 Mathematical Physics
Algebraic Geometry
math.MP
Abstract
We construct the first smooth embedded compact special Legendrian surfaces in of genus greater than one. More precisely, for every sufficiently large integer , we construct an embedded special Legendrian surface whose conformal structure is the Fermat curve of degree and genus . Our approach combines an elementary implicit function theorem with the description of special Legendrian surfaces via loop algebra-valued meromorphic connections and a characterization of the unitarizability locus in the -character variety of the thrice-punctured sphere.
Cite
@article{arxiv.2604.21521,
title = {Embedded special Legendrian surfaces in $\mathbb S^5$},
author = {Sebastian Heller and Franz Pedit and Charles Ouyang},
journal= {arXiv preprint arXiv:2604.21521},
year = {2026}
}
Comments
64 pages; comments welcome