拟凸Levi corank 1域的Gromov双曲性
Gromov hyperbolicity of pseudo-convex Levi corank one domains
摘要：
通过对Kobayashi度量的研究，我们证明了无限小Kobayashi度量和积分距离在不同尺度下的稳定性。作为应用，我们证明了有限型有界伪凸区域，其中每个边界点的Levi型都有余秩1，是关于Kobayashi度量的Gromov双曲。本文的结果推广了Zimmer和Fiacchi关于弱伪凸区域的Gromov双曲性的相关工作。
英文摘要：
After a study of the Kobayashi metrics on certain scaled domains, we show the stabilities of the infinitesimal Kobayashi metrics and the integrated distances in different scaling processes. As an application, we prove that bounded pseudo-convex domains of finite type where the Levi form of every boundary point has corank one are Gromov hyperbolic with respect to the Kobayashi metric. The results in this note generalize Zimmer's and Fiacchi's related works on Gromov hyperbolicity of weakly pseudo-convex domains.
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