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arXiv · 1709.08724

Mappings of finite distortion: compactness of the branch set

Aapo Kauranen·Rami Luisto·Ville Tengvall
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Abstract

We show that an entire branched cover of finite distortion cannot have a compact branch set if its distortion satisfies a certain asymptotic growth condition. We furthermore show that this bound is strict by constructing an entire, continuous, open and discrete mapping of finite distortion which is piecewise smooth, has a branch set homeomorphic to $(n-2)$-dimensional torus and distortion arbitrarily close to the asymptotic bound.

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Aapo Kauranen, Rami Luisto, Ville Tengvall. 2017-09-25. Mappings of finite distortion: compactness of the branch set. https://arxiv.org/abs/1709.08724

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