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SCHWARZIAN DERIVATIVES OF CONVEX MAPPINGS
(SUOMALAINEN TIEDEAKATEMIA, 2011)
A simple proof is given for Nehari's theorem that an analytic function f which maps the unit disk onto a convex region has Schwarzian norm parallel to f parallel to <= 2. The inequality in sharper form leads to the conclusion ...
Distortion Theorems Associated with Schwarzian Derivative for Harmonic Mappings
(SPRINGER BASEL AG, 2019)
Schwarzian norms and two-point distortion
(PACIFIC JOURNAL MATHEMATICS, 2011)
Distortion Theorems Associated with Schwarzian Derivative for Harmonic Mappings.
Let f be a complex-valued harmonic mapping defined in the unit disc D. The theorems of Chuaqui and Osgood (J Lond Math Soc 2:289–298, 1993), which assert that the bounds of the size of the hyperbolic norm of the Schwarzian ...
Criteria for univalence and quasiconformal extension of harmonic mappings in terms of the Schwarzian derivative.
We prove that if the Schwarzian norm of a given complex-valued locally univalent harmonic mapping f in the unit disk is small enough, then f is, indeed, globally univalent in the unit disk and can be extended to a ...
Distortion Theorems Associated with Schwarzian Derivative for Harmonic Mappings.
Let f be a complex-valued harmonic mapping defined in the unit disc D. The theorems of Chuaqui and Osgood (J Lond Math Soc 2:289–298, 1993), which assert that the bounds of the size of the hyperbolic norm of the Schwarzian ...
Affine and linear invariant families of harmonic mappings.
We study the order of affine and linear invariant families of planar harmonic mappings in the unit disk. By using the famous shear construction of Clunie and Sheil-Small, we construct a function to determine the order of ...
Schwarzian norms and two-point distortionPACIFIC JOURNAL OF MATHEMATICSPAC J MATH
(PACIFIC JOURNAL MATHEMATICS, 2016)
Distortion Theorems Associated with Schwarzian Derivative for Harmonic Mappings
(2019)
Let f be a complex-valued harmonic mapping defined in the unit disc D. The theorems of Chuaqui and Osgood (J Lond Math Soc 2:289-298, 1993), which assert that the bounds of the size of the hyperbolic norm of the Schwarzian ...