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 -dimensional cube onto itself, whose Jacobian is equal to 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}
}