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27th International Conference on Finite and Infinite Dimensional Complex Analysis and Applications
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A Gromov hyperbolic metric vs the hyperbolic and other related metrics S. Sahoo |
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Аннотация: We mainly consider two metrics: a Gromov hyperbolic metric and a scale invariant Cassinian metric. A metric space $$d(x,z)+d(y,w)\le (d(x,w)+d(y,z))\vee (d(x,y)+d(z,w))+2\beta $$ for all points For a domain $$ u_D(x,y)=2\log \frac{|x-y|+\max\{{\rm dist}(x,\partial D),{\rm dist}(y,\partial D)\}} {\sqrt{{\rm dist}(x,\partial D)\,{\rm dist}(y,\partial D)}}, \quad x,y\in D. $$ Ibragimov proved in [1] that the A scale invariant version of the Cassinian metric has been studied by Ibragimov in [2] which is defined by $$ \tilde{\tau}_D(x,y)=\log\left(1+\sup_{p\in \partial D}\frac{|x-y|}{\sqrt{|x-p||p-y|}}\right), \quad x,y\in D\subsetneq \mathbb{R}^n. $$ The interesting part of this metric is that many properties in arbitrary domains are revealed in the setting of once-punctured spaces. For example, Our purpose is to compare the This is a joint work with Manas Ranjan Mohapatra. Язык доклада: английский Список литературы
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