Article

Siberian Mathematical Journal

, Volume 44, Issue 6, pp 959-968

First online:

Linear Bilipschitz Extension Property

  • P. AlestaloAffiliated withTechnical University of Helsinki
  • , D. A. TrotsenkoAffiliated withSobolev Institute of Mathematics
  • , J. VaisalaAffiliated withUniversity of Helsinki

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Abstract

We give a sufficient geometric condition for a subset A of R n to enjoy the following property for a fixed C≥1: There is δ>0 such that for 0≤ε≤δ, each (1+ε)-bilipschitz map f: AR n extends to a (1+Cε)-bilipschitz map F: R n R n .

bilipschitz mapping quasi-isometry approximation extension of mappings subsets of Euclidean space