Conformal Dimension: Theory and Application

By J. M. Mackay, Jeremy T. Tyson. 2010

136 citations recorded by the source corpus.

Subfields: Atomic and Molecular Physics, and Optics, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/31a6a497bd8888da88ee05975886029cba9fd8a5

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In Atomic and Molecular Physics, and Optics

In Computational Theory and Mathematics

In Geometry and Topology

Citations in the corpus

Combinatorial modulus, the Combinatorial Loewner Property, and Coxeter groups (2010, background): “the infimum of Hausdorff dimensions of Ahlfors regular metric spaces quasi-Moebius homeomorphic to Z (see [MT10] for more details about conformal dimension).”
Diophantine approximation and the geometry of limit sets in Gromov hyperbolic metric spaces (2013, background): “at in this case. Proof of Proposition B.3. (i) The rst step is to write the visual metric on @X in terms of the sesquilinear form B. Indeed, direct calculation (for details see either [22] or p.32 of [47]) yields that for x;y 2@X, D 0(x;y) = D 0;e(x;y) = r 1 2 j1 h x;yij: We may dene a coordinate ch”
Quasisymmetric rigidity of square Sierpinski carpets (2011, background): “od helpless in front of these and other problems of quasiconformal geometry (another wellknown hard problem related to carpets is the question of the (Ahlfors regular) conformal dimension of S 3; see [MT] for general background and [Kig] for specic results on S 3). The main results of this paper giv”
Assouad Dimension and Fractal Geometry (2020, methodology): “Moreover, the definition we use, see the beginning of Chapter 2, was also adopted by Robinson [240] and Mackay and Tyson [195].”
On the conformal gauge of a compact metric space (2012, methodology): “We start by recalling some definitions, for a detailed exposition we refer to [MT10].”
Assouad dimension of self-affine carpets (2010, background): “We sketch the argument for the reader’s convenience; details are given in [6].”