论文标题
域的局部和全球可见性以及域的双曲线相对于Kobayashi距离
Local and global visibility and Gromov hyperbolicity of domains with respect to the Kobayashi distance
论文作者
论文摘要
我们介绍了本地可见和本地gromov双曲线域中的概念，其中$ \ mathbb c^d $。我们证明，$ \ mathbb c^d $中的一个有界域在本地可见，并且只有当它（全球）可见时，并且相对于Kobayashi距离（全球）杂音。这允许从边界附近的局部信息中检测到那些是Gromov双曲线的结构域，并且生物形态形态不断扩展到边界。
We introduce the notion of locally visible and locally Gromov hyperbolic domains in $\mathbb C^d$. We prove that a bounded domain in $\mathbb C^d$ is locally visible and locally Gromov hyperbolic if and only if it is (globally) visible and Gromov hyperbolic with respect to the Kobayashi distance. This allows to detect, from local information near the boundary, those domains which are Gromov hyperbolic and for which biholomorphisms extend continuously up to the boundary.
