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

2015/10/19 by Paweł Goldstein, Piotr Hajłasz, Goldstein, Paweł +1
Engineering · Mathematics · #26B10 #37A05 #Advanced Differential Equations and Dynamical Systems #Classical Analysis and ODEs (math.CA) #Control and Dynamics of Mobile Robots #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Primary 46E35 #Secondary 28D05

paper · pdf · doi:10.48550/arxiv.1510.05575

openalex publication_date 2015/10/19 · openalex created_date 2022/09/26 · openalex updated_date 2026/07/28

Abstract

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

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