Bi-Lipschitz approximation by finite-dimensional imbeddings

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