Bi-Lipschitz approximation by finite-dimensional imbeddings

Karin Usadi Katz, Mikhail G. Katz

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


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 languageEnglish
Pages (from-to)131-136
Number of pages6
JournalGeometriae Dedicata
Issue number1
StatePublished - Feb 2011

Bibliographical note

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


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


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