Isothermic constrained Willmore tori in 3-space

Abstract

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.

19 pages, 2 figures, originally Section 3 of arXiv:1901.05664, details added;