Search results for "branch sets"

showing 2 items of 2 documents

Mappings of finite distortion : size of the branch set

2018

Abstract We study the branch set of a mapping between subsets of ℝ n {\mathbb{R}^{n}} , i.e., the set where a given mapping is not defining a local homeomorphism. We construct several sharp examples showing that the branch set or its image can have positive measure.

Applied Mathematics010102 general mathematicsbranch setsTopology01 natural sciencesSet (abstract data type)funktioteoriamappings of finite distortionDistortion0103 physical sciences010307 mathematical physics0101 mathematicsAnalysisGeometry and topologyMathematics
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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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