Ahlfors-David regular sets and bilipschitz maps

Abstract

Given two Ahlfors-David regular sets in metric spaces, we study the question whether one of them has a subset bilipschitz equivalent with the other.

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• Rigidity Theorem of Graph-directed Fractals
• Bilipschitz embedding of homogeneous fractals
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• Dvoretzky-type theorem for Ahlfors regular spaces
• Lipschitz equivalence of self-similar sets with touching structures
• A mixed multifractal analysis for quasi Ahlfors vector-valued measures
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• Mixed multifractal densities for quasi-Ahlfors vector-valued measures