Mappings of Finite Distortion : Compactness of the Branch Set
Kauranen, A., Luisto, R., & Tengvall, V. (2018). Mappings of Finite Distortion : Compactness of the Branch Set. Preprint.
Päivämäärä
2018Oppiaine
MatematiikkaTekijänoikeudet
© the Authors, 2018.
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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