• Corpus ID: 239768296

Pointwise rotation for homeomorphisms with integrable distortion and controlled compression

@inproceedings{Hitruhin2021PointwiseRF,
  title={Pointwise rotation for homeomorphisms with integrable distortion and controlled compression},
  author={Lauri Hitruhin and Banhirup Sengupta},
  year={2021}
}
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 motivated by examples arising from fluid mechanics. We also present examples proving sharpness in a strong sense. 
View PDF on arXiv

References

SHOWING 1-10 OF 20 REFERENCES
Rotational properties of homeomorphisms with integrable distortion
  • L. Hitruhin
  • Mathematics
    Conformal Geometry and Dynamics of the American Mathematical Society
  • 2018
We establish a modulus inequality, with weak assumptions on the Sobolev regularity, for homeomorphisms with integrable distortion. As an application, we find upper bounds for the pointwise rotation…
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…
Sobolev regular flows of non-Lipschitz vector fields
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…
Mappings of finite distortion: Formation of cusps III
We give sharp integrability conditions on the distortion of a planar homeomorphism that maps a standard cusp onto the unit disk.
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…
On multifractal spectrum of quasiconformal mappings
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…
Elliptic Partial Differential Equations and Quasiconformal Mappings in the Plane (Pms-48)
This book explores the most recent developments in the theory of planar quasiconformal mappings with a particular focus on the interactions with partial differential equations and nonlinear analysis.…
Non-stationary flow of an ideal incompressible liquid
...
1
2
...