Search results for "LIGHT OPEN MAPS"

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Mappings of Finite Distortion : Compactness of the Branch Set

2017

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 an (n - 2)-dimensional torus and distortion arbitrarily close to the asymptotic bound. Peer reviewed

General Mathematicsbranch setsCOVERS01 natural sciencesfunktioteoriaSet (abstract data type)Mathematics - Geometric TopologyDimension (vector space)DistortionFOS: Mathematics111 Mathematicsfinite distortionComplex Variables (math.CV)topologia0101 mathematicsDIMENSIONMathematicsPartial differential equationMathematics - Complex Variables010102 general mathematicsMathematical analysisGeometric Topology (math.GT)TorusCompact spaceCover (topology)57M12 30C65PiecewiseLIGHT OPEN MAPSmonistotAnalysis
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