论文标题
希尔伯特几何形状中渐近测量学的凸角
Convexity of asymptotic geodesics in Hilbert Geometry
论文作者
论文摘要
如果$ω$是$ \ mathbb {r}^{2} $和$ f，g $两个渐近地球的内饰，我们表明距离函数$ d \ left（f \ left（f \ left（t \ weft（t \ oright），g \ weft（t \ weft（t \ right））$ t $ to $ t $ t $ t $ t $ t $ t $ t $ t $ t $ t $ t tofly tofly t $ t。在情况下，在$ c^{2} $的情况下获得了相同的结果，并且在$ f \ left（\ infty \ right）= g \ left（\ infty \ right）$时，$ \ partialω$的曲率不会消失。提供了曲率假设的必要性的示例。
If $Ω$ is the interior of a convex polygon in $\mathbb{R}^{2}$ and $f,g$ two asymptotic geodesics, we show that the distance function $d\left(f\left(t\right),g\left(t\right)\right)$ is convex for $t$ sufficiently large. The same result is obtained in the case $\partial Ω$ is of class $C^{2}$ and the curvature of $\partial Ω$ at the point $f\left(\infty\right)=g\left(\infty\right) $ does not vanish. An example is provided for the necessity of the curvature assumption.
