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.

中文翻译：

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等温约束在3空间中的Willmore花托

我们证明了3球中的均质和2瓣Delaunay花托提供了3空间中唯一等温约束的Willmore花托，Willmore能量低于\（8 \ pi \）。特别是，每个具有Willmore能量低于\（8 \ pi \）和非矩形保形类的受约束Willmore圆环都是不退化的。