Bi-Lipschitz approximation by finite-dimensional imbeddings
Differential Geometry
2009-02-24 v2 Logic
Abstract
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.
Cite
@article{arxiv.0902.3126,
title = {Bi-Lipschitz approximation by finite-dimensional imbeddings},
author = {Karin Usadi Katz and Mikhail G. Katz},
journal= {arXiv preprint arXiv:0902.3126},
year = {2009}
}
Comments
12 pages, 1 figure