We show that the class of quasisymmetric maps between horizontal self-affine carpets is rigid. Such maps can only exist when the dimensions of the carpets coincide, and in this case, the quasisymmetric maps are quasi-Lipschitz. We also show that horizontal self-affine carpets are minimal for the conformal Assouad dimension.peerReviewe
This thesis discusses three different projects concerning quasiconformal mappings on planar surfaces...
Quasiconformal mappings in space are known to have many rigidity proper-ties. For instance, 1.1. The...
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On a metric space, there are various classes of functions which respect aspects of the metric space ...
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The problem of quasiplanar maps between spaces with affine connection was set by N. S....
We consider the dimensions of a family of self-affine sets related to the Bedford-McMullen carpets. ...
This thesis discusses three different projects concerning quasiconformal mappings on planar surfaces...
Quasiconformal mappings in space are known to have many rigidity proper-ties. For instance, 1.1. The...
Abstract. Motivated by questions in geometric group theory we define a quasisymmetric co-Hopfian pro...
Abstract. We study a new class of square Sierpiński carpets Fn,p (5 ≤ n, 1 ≤ p < n2 − 1) on S2, ...
Abstract. We prove that every quasisymmetric self-homeomor-phism of the standard 1/3-Sierpiński car...
Abstract. We calculate the Assouad dimension of the self-affine carpets of Bedford and McMullen. We ...
We show that fiber-preserving quasisymmetric maps are biLipschitz. As an application, we show that q...
The Sierpinski gasket and other self-similar fractal subsets of Rd, d = 2, can be mapped by quasicon...
We calculate the Assouad dimension of a planar self-affine set X satisfying the strong separation co...
On a metric space, there are various classes of functions which respect aspects of the metric space ...
We prove a rigidity theorem that shows that, under many circumstances, quasi-isometric embeddings of...
We derive upper and lower bounds for the Assouad and lower dimensions of self-affine measures in ℝd ...
Abstract We study the conformal dimension of fractal percolation and show that, almost surely, the ...
The problem of quasiplanar maps between spaces with affine connection was set by N. S....
We consider the dimensions of a family of self-affine sets related to the Bedford-McMullen carpets. ...
This thesis discusses three different projects concerning quasiconformal mappings on planar surfaces...
Quasiconformal mappings in space are known to have many rigidity proper-ties. For instance, 1.1. The...
Abstract. Motivated by questions in geometric group theory we define a quasisymmetric co-Hopfian pro...
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