Two-Point Distortion Theorems for Harmonic Mappings

Víctor Bravo; Rodrigo Hernández; Osvaldo Venegas

doi:10.1007/s40840-023-01494-2

Two-Point Distortion Theorems for Harmonic Mappings

Víctor Bravo, Rodrigo Hernández, Osvaldo Venegas

Research output: Contribution to journal › Article › peer-review

Abstract

We establish two-point distortion theorems for sense-preserving planar harmonic mappings f= h+ g¯ in the unit disk D which satisfy harmonic versions of the univalence criteria due to Becker and Nehari. In addition, we also find two-point distortion theorems for the cases when h is a normalized convex function and, more generally, when h(D) is a c-linearly connected domain.

Original language	English
Article number	100
Journal	Bulletin of the Malaysian Mathematical Sciences Society
Volume	46
Issue number	3
DOIs	https://doi.org/10.1007/s40840-023-01494-2
State	Published - May 2023
Externally published	Yes

Keywords

Harmonic mappings
Two-point distortion
Univalence criterion

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10.1007/s40840-023-01494-2

Cite this

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abstract = "We establish two-point distortion theorems for sense-preserving planar harmonic mappings f= h+ g¯ in the unit disk D which satisfy harmonic versions of the univalence criteria due to Becker and Nehari. In addition, we also find two-point distortion theorems for the cases when h is a normalized convex function and, more generally, when h(D) is a c-linearly connected domain.",

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AB - We establish two-point distortion theorems for sense-preserving planar harmonic mappings f= h+ g¯ in the unit disk D which satisfy harmonic versions of the univalence criteria due to Becker and Nehari. In addition, we also find two-point distortion theorems for the cases when h is a normalized convex function and, more generally, when h(D) is a c-linearly connected domain.

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KW - Univalence criterion

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Two-Point Distortion Theorems for Harmonic Mappings

Abstract

Keywords

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