Research Article On Harmonic Quasiconformal Quasi-Isometries Page 1 Hindawi
Publishing Corporation Journal of Inequalities and Applications Volume 2010, Article ID …

We prove a global estimate for the gradient of the solution of the Poisson differential
inequality| Δ u (x)|≤ a| Du (x)| 2+ b, x∈ B n, where a, b<∞ and u| _ S^ n-1 ∈ C^ 1, α (S^ n …

We prove the following theorem: every quasiconformal harmonic mapping between two
plane domains with C1, α (α< 1) and, respectively, C1, 1 compact boundary is bi-Lipschitz …

Suppose that ℎ is a harmonic mapping of the unit disc onto a 𝐶1, 𝛼 domain 𝐷. We give
sufficient and necessary conditions in terms of boundary function that ℎ is qc We announce …

In this paper, our main aim is to discuss the properties of harmonic mappings in the unit ball
𝔹n. First, we characterize the harmonic Bloch spaces and the little harmonic Bloch spaces …

Let f= h+ g¯ be a univalent sense preserving harmonic mapping of the unit disk 𝕌 onto a
convex domain Ω. It is proved that: for every a such that| 𝑎|< 1 (resp.| 𝑎|= 1) the mapping f …

Suppose that ℎ is a harmonic mapping of the unit disc onto a 𝐶1, 𝛼 domain 𝐷. Then ℎ is qc
if and only if it is bi-Lipschitz. In particular, we consider sufficient and necessary conditions in …

We obtain a sharp estimate of the derivatives of harmonic quasiconformal extension u= P
[phi] of a Lipschitz map phi: Sn-1-> Rn. We also consider additional conditions which …

The following theorem is proved: If w is a quasi-conformal harmonic mapping between two
Riemann surfaces with compact and smooth boundaries and approximate analytic metrics …

Moduli of Continuity of Harmonic Quasiregular Mappings in Bn Page 1 Potential Anal (2011)
34:283–291 DOI 10.1007/s11118-010-9195-8 Moduli of Continuity of Harmonic Quasiregular …