Modulus of continuity of orientation preserving approximately differentiable homeomorphisms with a.e. negative Jacobian

Paweł Goldstein; Piotr Hajłasz

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arXiv · 1701.04348

Modulus of continuity of orientation preserving approximately differentiable homeomorphisms with a.e. negative Jacobian

Paweł Goldstein·Piotr Hajłasz

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Abstract

We construct an a.e. approximately differentiable homeomorphism of a unit $n$-dimensional cube onto itself which is orientation preserving, has the Lusin property (N) and has the Jacobian determinant negative a.e. Moreover, the homeomorphism together with its inverse satisfy a rather general sub-Lipschitz condition, in particular it can be bi-H\"older continuous with an arbitrary exponent less than $1$.

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Paweł Goldstein, Piotr Hajłasz. 2017-01-16. Modulus of continuity of orientation preserving approximately differentiable homeomorphisms with a.e. negative Jacobian. https://arxiv.org/abs/1701.04348

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