论文标题
Gromov双曲空间的呼吸功能边界
The horofunction boundary of a Gromov hyperbolic space
论文作者
论文摘要
我们在适当的GEODESIC GROMOV双曲线度空间上强调了一种条件，即接近的大地测量特性，这意味着呼吸函数紧凑型在拓扑上等同于Gromov紧凑型。众所周知，这种对等不变。我们证明使用重新制定技术表明，接近的大地测量属性通过$ \ mathbb {c}^q $的限制性pseudoconvex域满足了Kobayashi Metric。我们还表明，$ \ mathbb {C}^q $的有限凸域具有有限类型的边界，而d'Angelo的意义上满足了较弱的属性，这仍然意味着两个所述压实的等效性。结果，我们证明，在那些大小的holosperes上，由于Abate的定义。最后，我们概括了经典的朱莉娅的引理，并将其应用于非扩展地图的动力学。
We highlight a condition, the approaching geodesics property, on a proper geodesic Gromov hyperbolic metric space, which implies that the horofunction compactification is topologically equivalent to the Gromov compactification. It is known that this equivalence does not hold in general. We prove using rescaling techniques that the approaching geodesics property is satisfied by bounded strongly pseudoconvex domains of $\mathbb{C}^q$ endowed with the Kobayashi metric. We also show that bounded convex domains of $\mathbb{C}^q$ with boundary of finite type in the sense of D'Angelo satisfy a weaker property, which still implies the equivalence of the two said compactifications. As a consequence we prove that on those domains big and small horospheres as defined by Abate coincide. Finally we generalize the classical Julia's lemma, giving applications to the dynamics of non-expanding maps.
