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Separated nets in Euclidean space and Jacobians of biLipschitz maps

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Abstract.

We show that there are separated nets in the Euclidean plane which are not biLipschitz equivalent to the integer lattice. The argument is based on the construction of a continuous function which is not the Jacobian of a biLipschitz map.

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Authors and Affiliations

  1. Dept. of Mathematics, Pennsylvania State Univ., University Park, PA 16802-6401, USA, , , , , , US

    D. Burago

  2. Dept. of Mathematics, Univ. of Pennsylvania, Philadelphia, PA 19104, USA, , , , , , US

    B. Kleiner

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  1. D. Burago
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  2. B. Kleiner
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Submitted: April 1997

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Burago, D., Kleiner, B. Separated nets in Euclidean space and Jacobians of biLipschitz maps. GAFA, Geom. funct. anal. 8, 273–282 (1998). https://doi.org/10.1007/s000390050056

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  • DOI: https://doi.org/10.1007/s000390050056

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