Bi-Lipschitz approximation by finite-dimensional imbeddings

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We show that the Kuratowski imbedding of a Riemannian manifold in L^\infty, exploited in Gromov's proof of the systolic inequality for essential manifolds, admits an approximation by a (1+C)-bi-Lipschitz (onto its image), finite-dimensional imbedding for every C>0. Our key tool is the first variation formula thought of as a real statement in first-order logic, in the context of non-standard analysis.
12 pages, 1 figure

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Differential Geometry, Logic, 53C23, 26E35

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http://salesiana.dossiersoluciones.com/handle/123456789/221067

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0902.3126
 http://arxiv.org/abs/0902.3126

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arXiv