Hyperbolic Type Metrics

  • Vesna Todorčević


The natural setup for our work here is a metric space (G, mG) where G is a subdomain of \(\mathbb {R}^n\,, n\ge 2\). For our studies, the distance mG(x, y), x, y ∈ G is required to take into account both how close the points x, y are to each other and the position of the points relative to the boundary ∂G. Metrics of this type are called hyperbolic type metrics and they are substitutes for the hyperbolic metric in dimensions n ≥ 3. The quasihyperbolic metric and the distance ratio metric are both examples of hyperbolic type metrics. A key problem is to study a quasiconformal mapping between metric spaces
$$\displaystyle f: (G, m_G) \to (f(G), m_{f(G)}) $$
and to estimate its modulus of continuity. We expect Holder continuity, but a concrete form of these results may differ from metric to metric. Another question is the comparison of the metrics to each other.


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Authors and Affiliations

  • Vesna Todorčević
    • 1
    • 2
  1. 1.Faculty of Organizational SciencesUniversity of BelgradeBelgradeSerbia
  2. 2.Mathematical InstituteSerbian Academy of Sciences and ArtsBelgradeSerbia

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