Isometric approximation property of unbounded sets
We give a necessary and sufficient quantitative geometric condition for an unbounded set A ⊂ Rn to have the following property with a given c > 0: For every ε ≥ 0 and for every map f: A → Rn such that Open image in new window , there is an isometry T: A → Rn such that ¦Tx−fx¦ ≤ cε for all x ∈ A.
2000 Mathematics Subject Classification46C05 46B20 30C65
Key Wordsnearisometry Hyers-Ulam isometric approximation
Unable to display preview. Download preview PDF.
- [BL][BL] Y. Benyamini and J. Lindenstrauss, Geometric nonlinear functional analysis I, AMS Colloquium Publications 48, 2000.Google Scholar
- [Ma]E. Matoušková, Almost isometries of balls, J. Punct. Anal. 190 (2002) 505–525.Google Scholar
- [Re]E.G. Rees, Notes on geometry, Springer, 1983.Google Scholar
- [Vä2]J. Väisälä, A survey of nearisometries, Report. Univ. Jyväskylä 83 (2001), 305–315.Google Scholar