An analog of the Poincar´e metric and isoperimetric constants
https://doi.org/10.26907/0021-3446-2024-9-92-99
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.
About the Author
F. G. Avkhadiev
Kazan Federal University
Russian Federation
Russian Federation
Farit Gabidinovich Avkhadiev
18 Kremlyovskaya str., Kazan, 420008
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Review
For citations:
Avkhadiev F.G. An analog of the Poincar´e metric and isoperimetric constants. Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika. 2024;(9):92-99. (In Russ.) https://doi.org/10.26907/0021-3446-2024-9-92-99
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