Filippo Bracci, Hervé Gaussier, Nikolai Nikolov, Pascal Thomas
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引用次数: 0
摘要
在C d \mathbb {C}^d中引入了局部可见和局部Gromov双曲域的概念。我们证明了C d \mathbb {C}^d中的有界区域局部可见且局部Gromov双曲当且仅当它在Kobayashi距离上是(全局)可见且Gromov双曲。这允许从边界附近的局部信息中检测出那些是Gromov双曲的并且生物全纯态连续延伸到边界的域。
Local and global visibility and Gromov hyperbolicity of domains with respect to the Kobayashi distance
We introduce the notion of locally visible and locally Gromov hyperbolic domains in Cd\mathbb {C}^d. We prove that a bounded domain in Cd\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.
期刊介绍：
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