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Affine properties and injectivity of quasi-isometries

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Abstract

We approximateε-quasi-isometries between finite-dimensional Banach spaces by linear near-isometries. In this way we improve and extend a theorem of John. We also improve results of Gevirtz on injectivity criteria for quasi-isometries. Our approach is to show thatε-quasi-isometries almost satisfy the Jensen functional equation and to use then known facts about linear approximation of approximate solutions of Jensen’s equation.

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  1. Department of Mathematics, Technion — Israel Institute of Technology, 32000, Haifa, Israel

    I. A. Vestfrid

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  1. I. A. Vestfrid
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Vestfrid, I.A. Affine properties and injectivity of quasi-isometries. Isr. J. Math. 141, 185–210 (2004). https://doi.org/10.1007/BF02772218

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  • DOI: https://doi.org/10.1007/BF02772218

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