Univalence criterion for harmonic mappings and Φ-like functions

DOI10.1080/17476933.2017.1409741zbMath1401.30006arXiv1510.04886OpenAlexW2963108885MaRDI QIDQ4689841

Sergey Yu. Graf, Saminathan Ponnusamy, Victor V. Starkov

Publication date: 22 October 2018

Published in: Complex Variables and Elliptic Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1510.04886

zbMATH Keywords

univalent harmonic mappingsstar-likeclose-to-convex mappingsinvariant familiesdistortion and covering theorems

Mathematics Subject Classification ID

Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) (30C45) Harmonic, subharmonic, superharmonic functions in two dimensions (31A05) Quasiconformal mappings in the complex plane (30C62) Extremal problems for conformal and quasiconformal mappings, other methods (30C75)

Related Items (3)

Coefficients of univalent harmonic mappings ⋮ Sections of univalent harmonic mappings ⋮ The Jacobian conjecture and injectivity conditions

Cites Work

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• Harmonic univalent functions
• Variability regions for certain families of harmonic univalent mappings
• UNIVALENCE OF HARMONIC FUNCTIONS, PROBLEM OF PONNUSAMY AND SAIRAM, AND CONSTRUCTIONS OF UNIVALENT POLYNOMIALS
• Ahlfors's quasiconformal extension condition and $\Phi$-likeness
• 𝜙-like analytic functions. I

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