analysis / Calculus of variations
For $s \in (1/4,1)$ and any degree, the only $W^{s,1/s}$-minimizers among maps $\mathbb{S}^1 \to \mathbb{S}^1$ are Blaschke products. This resolves Open Problems 23 and 24 of Brezis and Mironescu's book on mappings to the circle, and Brezis's Favorite Open Problem 5.4 in the same range of $s$.
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in the range s in (1/4,1); Brezis's Problem 5.4 outside that range is untouched
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For $s \in (1/4,1)$ and any degree, the only $W^{s,1/s}$-minimizers among maps $\mathbb{S}^1 \to \mathbb{S}^1$ are Blaschke products. This resolves Open Problems 23 and 24 of Brezis and Mironescu's book on mappings to the circle, and Brezis's Favorite Open Problem 5.4 in the same range of $s$.
in the range s in (1/4,1); Brezis's Problem 5.4 outside that range is untouched
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