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These are critical points of the following nonlocal energy \\[ {\\mathcal{L}}_s(u)=\\int_{\\mathbb{R}^n}| ( {-\\Delta})^{\\frac{s}{2}} u(x)|^p dx\\,, \\] where $u\\in \\dot{H}^{s,p}(\\mathbb{R}^n,\\mathcal{N})$ and ${\\mathcal{N}}\\subset\\mathbb{R}^N$ is a closed $k$ dimensional smooth manifold and $s=\\frac{n}{p}$. We prove H\\\"older continuity for such critical points for $p \\leq 2$. For $p > 2$ we obtain the same under an additional Lorentz-space assumption. 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