On harmonic quasiconformal quasi-isometries.
Wiman and Arima theorems for quasiregular mappings.
On Jordan type inequalities for hyperbolic functions.
Ahlfors theorems for differential forms.
Conformal invariants in the punctured unit disk.
Singular values, Ramanujan modular equations, and Landen transformations
A new connection between geometric function theory and number theory is derived from Ramanujan’s work on modular equations. This connection involves the function recurrent in the theory of plane quasiconformal maps. Ramanujan’s modular identities yield numerous new functional identities for for various primes p.
Some inequalities for the Hersch-Pfluger distortion function.
Infinitesimal geometry of quasilinear mappings.
Self-similar Cantor sets and quasiregular mappings.
Embedding theorems for Bergman spaces in quasiconformal balls.
Submultiplicative properties of the -distortion function
Some inequalities related to the submultiplicative properties of the distortion function are derived.
Region of variability for spiral-like functions with respect to a boundary point
For μ ∈ ℂ such that Re μ > 0 let denote the class of all non-vanishing analytic functions f in the unit disk with f(0) = 1 and in . For any fixed z₀ in the unit disk, a ∈ ℂ with |a| ≤ 1 and λ ∈ ̅, we shall determine the region of variability V(z₀,λ) for log f(z₀) when f ranges over the class . In the final section we graphically illustrate the region of variability for several sets of parameters.
Estimates for the energy integral of quasiregular mappings on Riemannian manifolds and isoperimetry
The rate of growth of the energy integral of a quasiregular mapping is estimated in terms of a special isoperimetric condition on . The estimate leads to new Phragmén-Lindelöf type theorems.
On local injectivity and asymptotic linearity of quasiregular mappings
It is shown that the approximate continuity of the dilatation matrix of a quasiregular mapping f at implies the local injectivity and the asymptotic linearity of f at . Sufficient conditions for to behave asymptotically as are given. Some global injectivity results are derived.
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