Results 71 to 80 of about 353,858 (83)
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John domains and the quasihyperbolic metric
Complex Variables and Elliptic Equations, 1999David Herron
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Local convexity properties of quasihyperbolic balls in punctured space [PDF]
Journal of Mathematical Analysis and Applications, 2008 This paper deals with local convexity properties of the quasihyperbolic metric in the punctured space.
Riku Klen
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Quasihyperbolic metric and Quasisymmetric mappings in metric spaces
Transactions of the American Mathematical Society, 2015J. Väisälä has developed the theory of quasiconformal maps in the context of Banach spaces in a series of papers. For an overview of this work see [\textit{J. Väisälä}, Banach Cent. Publ. 48, 55--118 (1999; Zbl 0934.30018)]. The paper under review builds on these ideas. For instance the authors prove that the quasihyperbolic metric is invariant under a
Huang, Xiaojun, Liu, Jinsong
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Lφ(μ)-averaging domains and the quasi-hyperbolic metric [PDF]
Computers and Mathematics With Applications, 2004 In this paper, we first introduce Lℓ(μ)-averaging domains which are generalizations of existing domains, such as John domains and Ls(μ)-averaging domains. Then, we characterize Lφ(μ)-averaging domains using the quasihyperbolic metric.
Shusen Ding
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Domains with growth conditions for the quasihyperbolic metric
Journal d'Analyse Mathématique, 2000The quasihyperbolic metric \(k_D(x,y)\) is a counterpart of the standard hyperbolic metric on a plane domain on an arbitrary proper subdomain \(D\) of \(\mathbb{R}^n\) [{F. W. Gehring}, \textit{B. P. Palka}, J. Anal. Math. 30, 172-199 (1976; Zbl 0349.30019)]. For \(x\in D\) let \(\delta_D(x)\) be the distance from \(x\) to \(\partial D\).
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Siberian Mathematical Journal, 1999
It is well known that, in the Poincaré model (that is, in the half-space \(x_n >0\)), the metric of the hyperbolic (or Lobachevskij) space is given by the formula \[ ds^2=\frac{dx_1^2 + dx_2^2 +\dots +dx_n^2}{x_n^{2}}. \] Similarly, the metric, defined by the formula \[ ds^2=\frac{dx_1^2 + dx_2^2 +\dots +dx_n^2}{\rho (x)^{2}} \] in a domain \(D\subset \
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It is well known that, in the Poincaré model (that is, in the half-space \(x_n >0\)), the metric of the hyperbolic (or Lobachevskij) space is given by the formula \[ ds^2=\frac{dx_1^2 + dx_2^2 +\dots +dx_n^2}{x_n^{2}}. \] Similarly, the metric, defined by the formula \[ ds^2=\frac{dx_1^2 + dx_2^2 +\dots +dx_n^2}{\rho (x)^{2}} \] in a domain \(D\subset \
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The quasihyperbolic metric, growth, and John domains
1998The Hardy-Littlewood (H-L) theorem states that if \(f\) is analytic in the unit disk \(B\) and if \[ | f'(z)|\leq m\text{ dist}(z,\partial B)^{\alpha- 1},\tag ...
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Gromov Hyperbolicity, John Spaces, and Quasihyperbolic Geodesics
Journal of Geometric Analysis, 2022Yaxiang Li +2 more
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Quasihyperbolic Geodesics are Cone Arcs
Journal of Geometric Analysis, 2023Saminathan Ponnusamy, Qingshan Zhou
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Comparative Gromov hyperbolicity results for the hyperbolic and quasihyperbolic metrics
Complex Variables and Elliptic Equations, 2010Eva Touris Lojo +2 more
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