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Creators/Authors contains: "Fletcher, Alastair N"

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  1. ; (, Journal d'Analyse Mathématique)
    The Decomposition Problem in the class $$LIP(\S^2)$$ is to decompose any bi-Lipschitz map $$f:\S^2 \to \S^2$$ as a composition of finitely many maps of arbitrarily small isometric distortion. In this paper, we construct a decomposition for certain bi-Lipschitz maps which spiral around every point of a Cantor set $$X$$ of Assouad dimension strictly smaller than one. These maps are constructed by considering a collection of Dehn twists on the Riemann surface $$\S^2 \setminus X$$. The decomposition is then obtained via a bi-Lipschitz path which simultaneously unwinds these Dehn twists. As part of our construction, we also show that $$X \subset \S^2$$ is uniformly disconnected if and only if the Riemann surface $$\S^2 \setminus X$$ has a pants decomposition whose cuffs have hyperbolic length uniformly bounded above, which may be of independent interest. 
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  2. ; (, Mathematische Zeitschrift)
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