6533b7cffe1ef96bd12584d0

RESEARCH PRODUCT

Mappings of Finite Distortion : Compactness of the Branch Set

Rami LuistoRami LuistoAapo KauranenAapo KauranenVille TengvallVille Tengvall

subject

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

description

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

yearjournalcountryeditionlanguage
2017-09-25
http://urn.fi/URN:NBN:fi:jyu-201806283377