Bi-Lipschitz approximation by finite-dimensional imbeddings

Details Bi-Lipschitz approximation by finite-dimensional imbeddings Bi-Lipschitz approximation by finite-dimensional imbeddings

2009-02-18

arxiv.org/abs/0902.3126v2

Mathematics

Differential Geometry

12 pages, 1 figure

Scientific paper

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.

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