Mappings of Finite Distortion : Compactness of the Branch Set
Finna-arvio
Mappings of Finite Distortion : Compactness of the Branch Set
circlebranch2.pdf
(Jyväskylän yliopisto - JYX)
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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