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On the Willmore energy of Möbius bands
We show that among Möbius bands in $\mathbb{S}^3$ bounded by a great circle, the minimal Willmore energy is realized by an embedded minimal Möbius band with Morse index two. To prove this, we introduce a $2$-parameter ``canonical family" associated to any non-orientable surface in $\mathbb{S}^3$ wit
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