Papers by Vesna Manojlović
We characterize Gromov hyperbolicity of the quasihyperbolic metric space (\Omega,k) by geometric ... more We characterize Gromov hyperbolicity of the quasihyperbolic metric space (\Omega,k) by geometric properties of the Ahlfors regular length metric measure space (\Omega,d,\mu). The characterizing properties are called the Gehring--Hayman condition and the ball--separation condition.
Abstract and Applied Analysis, 2014
Proceedings of the American Mathematical Society, 2013
Bernoulli type inequalities for functions of logarithmic type are given. These functions include,... more Bernoulli type inequalities for functions of logarithmic type are given. These functions include, in particular, Gaussian hypergeometric functions in the zero-balanced case F (a, b; a + b; x) .
Journal of Mathematical Analysis and Applications, 2011
In this note we determine all numbers q ∈ R such that |u| q is a subharmonic function, provided t... more In this note we determine all numbers q ∈ R such that |u| q is a subharmonic function, provided that u is a K−quasiregular harmonic mappings in an open subset Ω of the Euclidean space R n .
Journal of Inequalities and Applications, 2011
We prove that for harmonic quasiconformal mappings α-Hölder continuity on the boundary implies α-... more We prove that for harmonic quasiconformal mappings α-Hölder continuity on the boundary implies α-Hölder continuity of the map itself. Our result holds for the class of uniformly perfect bounded domains, in fact we can allow that a portion of the boundary is thin in the sense of capacity. The problem for general bounded domains remains open.
Filomat, 2009
ABSTRACT We show that, for a class of moduli functions ω(δ), 0≤δ≤2, the property |φ(ξ)-φ(η)|≤ω(|ξ... more ABSTRACT We show that, for a class of moduli functions ω(δ), 0≤δ≤2, the property |φ(ξ)-φ(η)|≤ω(|ξ-η|), ξ,η∈S n-1 , implies the corresponding property |u(x)-u(y)|≤Cω(|x-y|), x,y∈B n , for u=P[φ], provided u is a quasiregular mapping. Our class of moduli functions includes ω(δ)=δ α , (0<α≤1), so our result generalizes earlier results on Hölder continuity and Lipschitz continuity.
Annales Academiae Scientiarum Fennicae Mathematica, 2010
We obtain a sharp estimate of the derivatives of harmonic quasiconformal extension u = P [φ] of a... more We obtain a sharp estimate of the derivatives of harmonic quasiconformal extension u = P [φ] of a Lipschitz map φ : S n−1 → R n . We also consider additional conditions which provide that u is Lipschitz on the unit ball; in particular, we give characterizations of Lipschitz continuity of u in the planar case and in the upper half space setting. We also answer a question posed by Martio in [OM] and extend this to the case of several variables. + = {(x, y) : x ∈ R n , y > 0} in Theorem 3.
Annales Academiae Scientiarum Fennicae Mathematica, 2013
We prove that ω u (δ) ≤ Cω f (δ), where u : Ω → R n is the harmonic extension of a continuous map... more We prove that ω u (δ) ≤ Cω f (δ), where u : Ω → R n is the harmonic extension of a continuous map f : ∂Ω → R n , if u is a K-quasiregular map and Ω is bounded in R n with C 2 boundary. Here C is a constant depending only on n, ω f and K and ω h denotes the modulus of continuity of h. We also prove a version of this result for Λ ω -extension domains with c-uniformly perfect boundary and quasiconformal mappings.
Potential Analysis, 2012
We prove that the composition of a quasi-nearly subharmonic function and a quasiregular mappings ... more We prove that the composition of a quasi-nearly subharmonic function and a quasiregular mappings of bounded multiplicity is quasi-nearly subharmonic. Also, we prove that if u • f is quasi-nearly subharmonic for all quasi-nearly subharmonic u and f satisfies some additional conditions, then f is quasiconformal. Similar results are further established for the class of regularly oscillating functions.
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Papers by Vesna Manojlović