论文标题
相对体积函数和球的能力在渐近双曲线歧管上
The relative volume function and the capacity of sphere on asymptotically hyperbolic manifolds
论文作者
论文摘要
在Li-shi-Aqing的工作之后，我们提出了AH流形的相对体积函数的定义。通常，这不是一个恒定的函数，我们研究了此功能的平均值。我们使用此函数来准确地表征给定边界指标的AH歧管的地球定义函数的高度。还证明，此类功能在无穷大的下方均匀地界定，并且仅取决于维度。作为应用程序，我们使用此功能来研究AH流动中球的能力，并提供一些限制结果。
Following the work of Li-Shi-Qing, we propose the definition of the relative volume function for an AH manifold. It is not a constant function in general and we study the egularity of this function. We use this function to give an accurate characterization of the height of the geodesic defining function for the AH manifold with a given boundary metric. It is also proved that such functions are uniformly bounded from below at infinity and the bound only depends on the dimension. As an application, we use this function to research the capacity of balls in AH manifold and provide some limit results.
