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

Felix Schlenk

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arXiv · math/0112260

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

Felix Schlenk

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Abstract

We 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.

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BibTeX RIS

Felix Schlenk. 2001-12-23. Volume preserving embeddings of open subsets of $R^n$ into manifolds. https://arxiv.org/abs/math/0112260

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