Volume preserving embeddings of open subsets of $R^n$ into manifolds

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62967We consider a connected smooth $n$-dimensional manifold $M$ endowed with a volume form $Ω$, and we show that an open subset $U$ of $R^n$ of Lebesgue measure $\Vol (U)$ embeds into $M$ by a smooth volume preserving embedding whenever the volume condition $\Vol (U) \le \Vol (M,Ω)$ is met.6 pagesDifferential Geometry58D20Volume preserving embeddings of open subsets of $R^n$ into manifoldstext