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Isothermic constrained Willmore tori in 3-space
Annals of Global Analysis and Geometry  (IF0.846),  Pub Date : 2021-05-20, DOI: 10.1007/s10455-021-09778-1
Lynn Heller, Sebastian Heller, Cheikh Birahim Ndiaye

We show that the homogeneous and the 2-lobe Delaunay tori in the 3-sphere provide the only isothermic constrained Willmore tori in 3-space with Willmore energy below $$8\pi$$. In particular, every constrained Willmore torus with Willmore energy below $$8\pi$$ and non-rectangular conformal class is non-degenerated.