论文标题
精确的准信息映射
Finely quasiconformal mappings
论文作者
论文摘要
我们介绍了准性的度量度定义的轻松版本，这对于低规律性的映射也很自然，包括$ w _ {\ mathrm {loc}}}^{1,1}（\ Mathbb {r}^n; \ Mathbb {r}^n; \ Mathbb {r}^n）$ - 型号。然后，我们在平面上表明，这种放松的定义可用于证明Sobolev的规律性，并且这些``精细的quasiconformal''映射实际上是准文化的。
We introduce a relaxed version of the metric definition of quasiconformality that is natural also for mappings of low regularity, including $W_{\mathrm{loc}}^{1,1}(\mathbb{R}^n;\mathbb{R}^n)$-mappings. Then we show on the plane that this relaxed definition can be used to prove Sobolev regularity, and that these ``finely quasiconformal'' mappings are in fact quasiconformal.
