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Khavinson conjecture for hyperbolic harmonic functions on the unit ball
Adel Khalfallah, Fathi Haggui, Miodrag Mateljević
In this paper, we prove the Khavinson conjecture for hyperbolic harmonic functions on the unit ball. This conjecture was partially solved in \cite{JKM2020}.
Schwarz lemmas for mappings with bounded Laplacian
Miodrag Mateljević, Adel Khalfallah
We establish some Schwarz type Lemmas for mappings defined on the unit disk with bounded Laplacian. Then we apply these results to obtain boundary versions of the Schwarz lemma.
Hyperbolic metric on the strip and the Schwarz lemma for HQR mappings
Miodrag Mateljević, Marek Svetlik
We give simple proofs of various versions of the Schwarz lemma for real valued harmonic functions and for holomorphic (more generally harmonic quasi\-re\-gu\-lar, shortly HQR) mapp…
Schwarz lemma and distortion for harmonic functions via length and area
Miodrag Mateljević
We give sharp estimates for distortion of harmonic by means of area and length of the corresponding surface.
The lower bound for the modulus of the derivatives and Jacobian of harmonic injective mappings
Miodrag Mateljević
We give the lower bound for the modulus of the radial derivatives and Jacobian of harmonic injective mappings from the unit ball onto convex domain in plane and space. As an applic…