• DOI:10.5186/AASFM.2016.4138
• Corpus ID: 54852646

On multifractal spectrum of quasiconformal mappings

@article{Hitruhin2016OnMS,
  title={On multifractal spectrum of quasiconformal mappings},
  author={Lauri Hitruhin},
  journal={Annales Academiae Scientiarum Fennicae. Mathematica},
  year={2016},
  volume={41},
  pages={503-522}
}

• L. Hitruhin
• Published 2016
• Mathematics
• Annales Academiae Scientiarum Fennicae. Mathematica

which can be calculated to have stretch α and rotation γ at the origin along any sequence (rn). We can say, roughly speaking, that mapping f satisfies (1.1) at some point z if f stretches and rotates at this point z, along some scales that decrease to zero, like the mapping fα(1+iγ) does at the origin. Given a mapping f and parameters α, γ we denote by Ef = Ef,α,γ the set of points that satisfy (1.1). For the Hausdorff dimension of these sets the following sharp result is given in [2]. Theorem 1.1. [2, Theorem 5.1] Let f : C → C be aK-quasiconformal mapping, with K > 1, and parameters α > 0 and γ ∈ R be such that α(1 + iγ) ∈ BK , where