Bohr Radius for Subordination and K-quasiconformal Harmonic Mappings

Harmonic Quasiconformal Mappings of Riemannian Manifolds

Quasiconformal Extension of Harmonic Mappings in the Plane

Let f be a sense-preserving harmonic mapping in the unit disk. We give a sufficient condition in terms of the pre-Schwarzian derivative of f to ensure that it can be extended to a quasiconformal map in the complex plane. Introduction A well-known criterion due to Becker [5] states that if a locally univalent analytic function φ in the unit disk D satisfies (1) sup z∈D ∣∣∣∣φ′′(z) φ′(z) ∣∣∣∣ (1− ...

On Harmonic Quasiconformal Self-mappings of the Unit Ball

It is proved that any family of harmonic K-quasiconformal mappings {u = P [f ], u(0) = 0} of the unit ball onto itself is a uniformly Lipschitz family providing that f ∈ C. Moreover, the Lipschitz constant tends to 1 as K → 1.

The Bohr Radius Of

We show that the Bohr radius of the polydisk D behaves asymptotically as √ (logn)/n. Our argument is based on a new interpolative approach to the Bohnenblust–Hille inequalities which allows us to prove, among other results, that the polynomial Bohnenblust–Hille inequality is subexponential.

Convex functions and quasiconformal mappings

Continuing our investigation of quasiconformal mappings with convex potentials, we obtain a new characterization of quasiuniformly convex functions and improve our earlier results on the existence of quasiconformal mappings with prescribed sets of singularities.