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A Measure and Orientation Preserving Homeomorphism with Approximate Jacobian Equal −1 Almost Everywhere

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Abstract

We construct an almost everywhere approximately differentiable, orientation and measure preserving homeomorphism of a unit n-dimensional cube onto itself, whose Jacobian is equal to −1 almost everywhere. Moreover, we prove that our homeomorphism can be uniformly approximated by orientation and measure preserving diffeomorphisms.

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Authors and Affiliations

  1. Institute of Mathematics, Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Banacha 2, 02-097, Warsaw, Poland

    Paweł Goldstein

  2. Department of Mathematics, University of Pittsburgh, 301 Thackeray Hall, Pittsburgh, PA, 15260, USA

    Piotr Hajłasz

Authors
  1. Paweł Goldstein
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  2. Piotr Hajłasz
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Corresponding author

Correspondence to Piotr Hajłasz.

Additional information

Communicated by A. Braides

P.G. was supported by FNP Grant POMOST BIS/2012-6/3.

P.H. was supported by NSF Grant DMS-1500647.

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Goldstein, P., Hajłasz, P. A Measure and Orientation Preserving Homeomorphism with Approximate Jacobian Equal −1 Almost Everywhere. Arch Rational Mech Anal 225, 65–88 (2017). https://doi.org/10.1007/s00205-017-1085-4

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  • DOI: https://doi.org/10.1007/s00205-017-1085-4

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