Geodesic
An analog of the Poincaré metric and isoperimetric constants
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2024), pp. 92-99 Cet article a éte moissonné depuis la source Math-Net.Ru

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For plane domains we define a new metric close to the Poincaré 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.
Mots-clés : Poincaré metric
Keywords: hyperbolic radius, isoperimetric inequality, uniformly perfect set. 
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     author = {F. G. Avkhadiev},
     title = {An analog of the {Poincar\'e} metric and isoperimetric constants},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {92--99},
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     url = {http://geodesic.mathdoc.fr/item/IVM_2024_9_a8/}
}
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F. G. Avkhadiev. An analog of the Poincaré metric and isoperimetric constants. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2024), pp. 92-99. http://geodesic.mathdoc.fr/item/IVM_2024_9_a8/

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