Year: 2024
Type: article
Abstract: For plane domains we define a new metric close to the Poincar\'{e} metric with the Gaussian curvature $k=-4$. For this quasi-hyperbolic metric we study inequalities of isoperimetric type. It is proved that the constant of the linear quasi-hyperbolic isoperimetric inequality for admissible subdomains of a given domain is finite if and only if the domain does not contain the point at infinity and has a uniformly perfect boundary. Also, we give estimates of these constants using some known numerical characteristics of domains.
Source: Russian Mathematics
Author: F. G. Avkhadiev
Institution: Kazan Federal University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4402873776