词条 | Conformal dimension |
释义 |
In mathematics, the conformal dimension of a metric space X is the infimum of the Hausdorff dimension over the conformal gauge of X, that is, the class of all metric spaces quasisymmetric to X.[1] Formal definitionLet X be a metric space and be the collection of all metric spaces that are quasisymmetric to X. The conformal dimension of X is defined as such PropertiesWe have the following inequalities, for a metric space X: The second inequality is true by definition. The first one is deduced from the fact that the topological dimension T is invariant by homeomorphism, and thus can be defined as the infimum of the Hausdorff dimension over all spaces homeomorphic to X. Examples
See also
References1. ^John M. Mackay, Jeremy T. Tyson, Conformal Dimension : Theory and Application, University Lecture Series, Vol. 54, 2010, Rhodes Island 3 : Fractals|Metric geometry|Dimension theory |
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