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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Volume preserving embeddings of open subsets of ${\mathbb R}^n$ into manifolds


Author: Felix Schlenk
Journal: Proc. Amer. Math. Soc. 131 (2003), 1925-1929
MSC (2000): Primary 58D20; Secondary 53C42, 57R40, 57D40
Published electronically: November 6, 2002
MathSciNet review: 1955282
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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.


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Additional Information

Felix Schlenk
Affiliation: Department of Mathematics, ETH Zürich, CH-8092 Zürich, Switzerland
Email: schlenk@math.ethz.ch

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06845-4
PII: S 0002-9939(02)06845-4
Received by editor(s): January 12, 2002
Published electronically: November 6, 2002
Communicated by: Jozef Dodziuk
Article copyright: © Copyright 2002 American Mathematical Society