Bi-Lipschitz approximation by finite-dimensional imbeddings

Karin Usadi Katz; Mikhail G. Katz

doi:10.1007/s10711-010-9497-4

Bi-Lipschitz approximation by finite-dimensional imbeddings

Karin Usadi Katz, Mikhail G. Katz

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

Gromov's celebrated systolic inequality from '83 is a universal volume lower bound in terms of the least length of a noncontractible loop in M. His proof passes via a strongly isometric imbedding called the Kuratowski imbedding, into the Banach space of bounded functions on M. We show that the imbedding admits an approximation by a (1+ε)-bi-Lipschitz (onto its image), finite-dimensional imbedding for every ε > 0, using the first variation formula and the mean value theorem.

Original language	English
Pages (from-to)	131-136
Number of pages	6
Journal	Geometriae Dedicata
Volume	150
Issue number	1
DOIs	https://doi.org/10.1007/s10711-010-9497-4
State	Published - Feb 2011

Bibliographical note

Funding Information:
Supported by the Israel Science Foundation (grants no. 84/03 and 1294/06) and the BSF (grant 2006393).

Keywords

Essential manifold
Finite-dimensional approximation
First variation formula
Geodesic
Gromov's inequality
Infinitesimal
Injectivity radius
Kuratowski imbedding
Systole
Systolic inequality

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Bi-Lipschitz approximation by finite-dimensional imbeddings

Abstract

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Keywords

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