Geodesic
Weak Capacity and Modulus Comparability in Ahlfors Regular Metric Spaces
Analysis and Geometry in Metric Spaces, Tome 4 (2016) no. 1 Cet article a éte moissonné depuis la source The Polish Digital Mathematics Library

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Let (Z, d, μ) be a compact, connected, Ahlfors Q-regular metric space with Q > 1. Using a hyperbolic filling of Z,we define the notions of the p-capacity between certain subsets of Z and of theweak covering p-capacity of path families Γ in Z.We show comparability results and quasisymmetric invariance.As an application of our methodswe deduce a result due to Tyson on the geometric quasiconformality of quasisymmetric maps between compact, connected Ahlfors Q-regular metric spaces.
Mots-clés : Weak capacity, weak covering capacity, modulus, quasisymmetry, quasi-isometry, Ahlfors regularmetric space, Gromov hyperbolic metric space, Ahlfors regular conformal dimension 
@article{AGMS_2016_4_1_a4,
     author = {Lindquist, Jeff},
     title = {Weak {Capacity} and {Modulus} {Comparability} in {Ahlfors} {Regular} {Metric} {Spaces}},
     journal = {Analysis and Geometry in Metric Spaces},
     year = {2016},
     volume = {4},
     number = {1},
     zbl = {06682298},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AGMS_2016_4_1_a4/}
}
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Lindquist, Jeff. Weak Capacity and Modulus Comparability in Ahlfors Regular Metric Spaces. Analysis and Geometry in Metric Spaces, Tome 4 (2016) no. 1. http://geodesic.mathdoc.fr/item/AGMS_2016_4_1_a4/