English

A submultiplicative property of the Carath\'eodory metric on planar domains

Complex Variables 2019-05-28 v1

Abstract

Given a pair of smoothly bounded domains D1,D2CD_1, D_2 \subset \mathbb C, the purpose of this note is to obtain an inequality that relates the Carath\'{e}odory metrics on D1,D2,D1D2D_1, D_2, D_1 \cap D_2 and D1D2D_1 \cup D_2.

Keywords

Cite

@article{arxiv.1905.10785,
  title  = {A submultiplicative property of the Carath\'eodory metric on planar domains},
  author = {Amar Deep Sarkar and Kaushal Verma},
  journal= {arXiv preprint arXiv:1905.10785},
  year   = {2019}
}