Volume preserving embeddings of open subsets of Rⁿ into manifolds

الأصل · EN

We consider a connected smooth n-dimensional manifold M endowed with a volume form Ω, and we show that an open subset U of Rⁿ of Lebesgue measure (U) embeds into M by a smooth volume preserving embedding whenever the volume condition (U) ≤ (M,Ω) is met.