标题： 拟共形映射和$\tfrac {dDf}{d|Df|}$在$f\in BV(\mathbb{R}^n; \mathbb{R}^n)$中的秩 显示英文标题

标题： Quasiconformal mappings and the rank of $\tfrac {dDf}{d|Df|}$ for $f\in BV(\mathbb{R}^n; \mathbb{R}^n)$

摘要： We define a relaxed version $H_f^{\textrm{fine}}$ of the distortion number $H_f$ that is used to define quasiconformal mappings. Then we show that for a BV function $f\in BV(\mathbb{R}^n;\mathbb{R}^n)$, for $|Df|$-a.e. $x\in\mathbb{R}^n$ it holds that $H_{f^*}^{\textrm{fine}}(x)<\infty$ if and only if $\tfrac{dDf}{d|Df|}(x)$ has full rank. 显示英文摘要

摘要： We define a relaxed version $H_f^{\textrm{fine}}$ of the distortion number $H_f$ that is used to define quasiconformal mappings. Then we show that for a BV function $f\in BV(\mathbb{R}^n;\mathbb{R}^n)$, for $|Df|$-a.e. $x\in\mathbb{R}^n$ it holds that $H_{f^*}^{\textrm{fine}}(x)<\infty$ if and only if $\tfrac{dDf}{d|Df|}(x)$ has full rank.