On multifractal spectrum of quasiconformal mappings

  title={On multifractal spectrum of quasiconformal mappings},
  author={Lauri Hitruhin},
  journal={Annales Academiae Scientiarum Fennicae. Mathematica},
  • 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… 
Stretching and rotation sets of quasiconformal mappings
  • Tyler Bongers
  • Mathematics
    Annales Academiae Scientiarum Fennicae Mathematica
  • 2019
Quasiconformal maps in the plane are orientation preserving homeomorphisms that satisfy certain distortion inequalities; infinitesimally, they map circles to ellipses of bounded eccentricity. Such
Joint rotational and stretching multifractal spectra of mappings with integrable distortion
  • L. Hitruhin
  • Mathematics
    Revista Matemática Iberoamericana
  • 2019
We establish bounds for both the stretching and the rotational multifractal spectra of planar homeomorphic mappings with p-integrable distortion. Moreover, we show that these bounds are sharp by
Fe b 20 21 Rotation bounds for Hölder continuous homeomorphisms with integrable distortion
We obtain sharp rotation bounds for the subclass of homeomorphisms f : C → C of finite distortion which have distortion function in Lploc, p > 1, and for which a Hölder continuous inverse is
Pointwise rotation for homeomorphisms with integrable distortion and controlled compression
We obtain sharp rotation bounds for homeomorphisms f : C → C whose distortion is in Lploc, p ≥ 1, and whose inverse have controlled modulus of continuity. The interest in this class is partially
Dimension compression and expansion under homeomorphisms with exponentially integrable distortion
. We improve both dimension compression and expansion bounds for homeomorphisms with p -exponentially integrable distortion. To the first direction we also introduce estimates for the compression
Rotation bounds for H\"older continuous homeomorphisms with integrable distortion
We obtain sharp rotation bounds for the subclass of homeomorphisms $f:\mathbb{C}\to\mathbb{C}$ of finite distortion which have distortion function in $L^p_{loc}$, $p>1$, and for which a Holder


Sharp Examples for Planar Quasiconformal Distortion of Hausdorff Measures and Removability
In the celebrated paper [5, Acta Mathematica, 173, 1994], Astala showed optimal area distortion bounds and dimension distortion estimates for planar quasiconformal mappings. He asked (Question 4.4)
Bilipschitz and quasiconformal rotation, stretching and multifractal spectra
We establish sharp bounds for simultaneous local rotation and Hölder-distortion of planar quasiconformal maps. In addition, we give sharp estimates for the corresponding joint quasiconformal
Pointwise rotation for mappings with exponentially integrable distortion
We prove an upper bound for pointwise rotation of mappings with $p$-exponentially integrable distortion. We also show that this bound is essentially optimal by providing examples which attain this
Elliptic Partial Differential Equations And Quasiconformal Mappings In The Plane Pms 48
Thank you very much for reading elliptic partial differential equations and quasiconformal mappings in the plane pms 48. Maybe you have knowledge that, people have look numerous times for their