English

A measure and orientation preserving homeomorphism with approximate Jacobian equal $-1$ almost everywhere

Classical Analysis and ODEs 2017-01-24 v2 Dynamical Systems

Abstract

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

Keywords

Cite

@article{arxiv.1510.05575,
  title  = {A measure and orientation preserving homeomorphism with approximate Jacobian equal $-1$ almost everywhere},
  author = {Paweł Goldstein and Piotr Hajłasz},
  journal= {arXiv preprint arXiv:1510.05575},
  year   = {2017}
}