Volume preserving embeddings of open subsets of ${\mathbb R}^n$ into manifolds
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- by Felix Schlenk
- Proc. Amer. Math. Soc. 131 (2003), 1925-1929
- DOI: https://doi.org/10.1090/S0002-9939-02-06845-4
- Published electronically: November 6, 2002
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Abstract:
We consider a connected smooth $n$-dimensional manifold $M$ endowed with a volume form $\Omega$, and we show that an open subset $U$ of ${\mathbb R}^n$ of Lebesgue measure $\operatorname {Vol}\;\! (U)$ embeds into $M$ by a smooth volume preserving embedding whenever the volume condition $\operatorname {Vol}\;\! (U) \le \operatorname {Vol}\;\!(M, \Omega )$ is met.References
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Bibliographic Information
- Felix Schlenk
- Affiliation: Department of Mathematics, ETH Zürich, CH-8092 Zürich, Switzerland
- MR Author ID: 673534
- Email: schlenk@math.ethz.ch
- Received by editor(s): January 12, 2002
- Published electronically: November 6, 2002
- Communicated by: Jozef Dodziuk
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 1925-1929
- MSC (2000): Primary 58D20; Secondary 53C42, 57R40, 57D40
- DOI: https://doi.org/10.1090/S0002-9939-02-06845-4
- MathSciNet review: 1955282