Triangular ratio metric under quasiconformal mappings in sector domains

Triangular ratio metric in the unit disk

The triangular ratio metric is studied in a domain $G\subsetneq\mathbb{R}^n$, $n\geq2$. Several sharp bounds are proven for this metric, especially, in the case where the domain is the unit disk of the complex plane. The results are applied to study the Hölder continuity of quasiconformal mappings.

关于视角度量的几点注记

Some remarks on the visual angle metric

证明了在凸区域中视角度量和三角形比率度量具有可比性。利用双曲几何的构造方法，我们还找到了半空间和球中视角度量的极值点。进一步研究了拟共形映射关于三角比度量和视角度量的畸变性质。

Intrinsic metrics under conformal and quasiregular mappings

The distortion of six different intrinsic metrics and quasi-metrics under conformal and quasiregular mappings is studied in a few simple domains $G\subsetneq\mathbb{R}^n$. The already known inequalities between the hyperbolic metric and these intrinsic metrics for points $x,y$ in the unit ball $\mathbb{B}^n$ are improved by limiting the absolute values of the points $x,y$ and the new results are then used to study the conformal distortion of the intrinsic metrics. For the triangular ratio metric between two points $x,y\in\mathbb{B}^n$, the conformal distortion is bounded in terms of the hyperb…

一种新的双曲型度量的几何性质

Geometric properties of a new hyperbolic type metric

研究在度量空间中引入的新距离函数\(\tilde{S}_{G,c}\)，证明\(c\geq2\)时它是度量且条件严格，探究其几何性质，如与三角比度量的关系、度量球包含关系，还研究了双利普希茨映射拟共形性及在莫比乌斯变换下的畸变性质。