English

Boundary behaviour of the Span metric and its higher-order curvatures

Complex Variables 2020-12-01 v1

Abstract

In this note, we use scaling principle to study the boundary behaviour of the span metric and its higher-order curvatures on finitely connected Jordan planar domains. A localization of this metric near boundary points of finitely connected Jordan domains is also obtained. Further, we obtain boundary sharp estimates for this metric on C2 C^2 -smooth bounded domains and consequently, this metric is comparable to the Carath\'eodory and the Kobayashi metrics on these domains.

Keywords

Cite

@article{arxiv.2011.15022,
  title  = {Boundary behaviour of the Span metric and its higher-order curvatures},
  author = {Amar Deep Sarkar},
  journal= {arXiv preprint arXiv:2011.15022},
  year   = {2020}
}