6533b874fe1ef96bd12d606a

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Homeomorphisms of finite distortion: discrete length of radial images

Tomi NieminenPekka Koskela

subject

Unit sphereDistortion (mathematics)Finite volume methodIntegrable systemDimension (vector space)General MathematicsMathematical analysisA domainGeometryGauge (firearms)Mathematics

description

AbstractWe study homeomorphisms of finite exponentially integrable distortion of the unit ball Bn onto a domain Ω of finite volume. We show that under such a mapping the images of almost all radii (in terms of a gauge dimension) have finite discrete length. We also show that our dimension estimate is essentially sharp.

https://doi.org/10.1017/s0305004107000734