Isometric approximation

Suppose thatA ⊂Rn is a bounded set of diameter 1 and that:f:A →l2 is a map satisfying the nearisometry condition |x−y|−ɛ≤|fx−fy|≤|x−y|+ɛ withɛ≤1. Then there is an isometryS:A →l2 such that |Sx−fx|≤cn √ɛ for allx inA. IfA satisfies a thickness condition and iff:A →Rn, then there is an isometryS:Rn →R...

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Bibliographic Details
Published in:Israel journal of mathematics 2001-01, Vol.125 (1), p.61-82
Main Authors: Alestalo, P., Trotsenko, D. A., Väisälä, J.
Format: Article
Language:English
Subjects:
Diameters
Mathematics
Thickness
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Summary:Suppose thatA ⊂Rn is a bounded set of diameter 1 and that:f:A →l2 is a map satisfying the nearisometry condition |x−y|−ɛ≤|fx−fy|≤|x−y|+ɛ withɛ≤1. Then there is an isometryS:A →l2 such that |Sx−fx|≤cn √ɛ for allx inA. IfA satisfies a thickness condition and iff:A →Rn, then there is an isometryS:Rn →Rn with |Sx−fx|≤cnɛ/q, whereq is a thickness parameter.
ISSN:0021-2172
1565-8511
DOI:10.1007/BF02773375