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I had asked the following question on math.stackexchange but did not get any response:

I'm looking for a reference which states the Sobolev embedding theorems on Riemann manifolds for fractional Sobolev spaces.

The references I know either don't deal with fractional spaces, or don't deal with manifolds.

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For the case of Riemannian manifolds, Hebey wrote a book about it. The main takeaway for Sobolev embeddings(not Morrey): If M is compact, everything is quite fine and works as usually. If M is only complete, the situation is a bit different (depends on curvature). For the general case, I unfortunately don't have a reference.

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