论文标题
$ \ mathbb {c}^2 $中的pseudoconvex有限类型域的gromov双曲线
Gromov hyperbolicity of pseudoconvex finite type domains in $\mathbb{C}^2$
论文作者
论文摘要
我们证明，有限的d'Angelo类型的每个有限的平滑域中的$ \ Mathbb {C}^2 $带有Kobayashi距离的每个有限的平滑域是Gromov双曲线，其Gromov边界在欧几里得边界上是同质的。我们还表明，$ \ mathbb {c}^2 $中的任何域都以kobayashi距离为gromov双曲线，前提是存在一系列自动形态，这些序列会收敛到有限的d'Angelo类型的平滑边界点。
We prove that every bounded smooth domain of finite d'Angelo type in $\mathbb{C}^2$ endowed with the Kobayashi distance is Gromov hyperbolic and its Gromov boundary is canonically homeomorphic to the Euclidean boundary. We also show that any domain in $\mathbb{C}^2$ endowed with the Kobayashi distance is Gromov hyperbolic provided there exists a sequence of automorphisms that converges to a smooth boundary point of finite D'Angelo type.
