论文标题
在渐近谐波空间中霍斯磷的交叉点上的两个定理
Two theorems on the intersections of horospheres in asymptotically harmonic spaces
论文作者
论文摘要
我们使用Busemann函数来构建在渐近谐波中保存映射的体积。如果渐近谐波流形满足可见性条件，我们构建映射，以在某些方向上保持距离。我们还证明，霍斯群交点上的一些积分与相应的Busemann函数值之间的差异无关，我们建立了两个holospheres相交体积的上限，这与相应的Busemann函数的值之间的差异无关。
We use Busemann functions to construct volume preserving mappings in an asymptotically harmonic manifold. If the asymptotically harmonic manifold satisfies the visibility condition, we construct mappings which preserve distances in some directions. We also prove that some integrals on the intersection of horospheres are independent of the differences between the values of the corresponding Busemann functions and we establish an upper bound of the volume of the intersection of two horospheres which is independent of the difference between values of corresponding Busemann functions.
