证明了保向近似可微同胚的Modulus of continuity，其中a.e.负雅可比矩阵
Modulus of continuity of orientation preserving approximately differentiable homeomorphisms with a.e. negative Jacobian
摘要：
我们建立一个a.e.单位$n$维立方体到自身上的近似可微同胚，它是方向保持的，具有Lusin性质（N），并且雅可比行列式为负a.e.此外，同胚及其逆满足一个相当一般的次利普希茨条件，特别是它可以是双Hölder连续的，其指数小于$1$。
英文摘要：
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-Hölder continuous with an arbitrary exponent less than $1$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
