论文标题
关于准构映射的平均半径
On the mean radius of quasiconformal mappings
论文作者
论文摘要
我们研究了准构映射的平均半径生长函数。我们在$ \ mathbb {r}^n $中给出了新的准信息映射，以$ n \ geq 2 $，称为有限的集成参数化映射，或简称为BIP映射。这些属性的属性是，Zorich转换为每个切片的限制在$ l^{n/（n-1）} $中具有统一的界限。对于BIP图，平均半径函数的对数变换为Bi-Lipschitz。然后，我们将结果应用于具有简单的无穷小空间的BIP图，以表明渐近表示确实是准信息，表明其Zorich Transform是Bi-Lipschitz地图。
We study the mean radius growth function for quasiconformal mappings. We give a new sub-class of quasiconformal mappings in $\mathbb{R}^n$, for $n\geq 2$, called bounded integrable parameterization mappings, or BIP maps for short. These have the property that the restriction of the Zorich transform to each slice has uniformly bounded derivative in $L^{n/(n-1)}$. For BIP maps, the logarithmic transform of the mean radius function is bi-Lipschitz. We then apply our result to BIP maps with simple infinitesimal spaces to show that the asymptotic representation is indeed quasiconformal by showing that its Zorich transform is a bi-Lipschitz map.
