Univalent harmonic mappings and linearly connected domains

M. Chuaqui; R. Hernández

doi:10.1016/j.jmaa.2006.10.086

Univalent harmonic mappings and linearly connected domains

M. Chuaqui, R. Hernández

Faculty of Engineering and Science

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

31 Scopus citations

Abstract

We investigate the relationship between the univalence of f and of h in the decomposition f = h + over(g, -) of a sense-preserving harmonic mapping defined in the unit disk D ⊂ C. Among other results, we determine the holomorphic univalent maps h for which there exists c > 0 such that every harmonic mapping of the form f = h + over(g, -) with | g^′ | < c | h^′ | is univalent. The notion of a linearly connected domain appears in our study in a relevant way.

Original language	English
Pages (from-to)	1189-1194
Number of pages	6
Journal	Journal of Mathematical Analysis and Applications
Volume	332
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2006.10.086
State	Published - 15 Aug 2007

Keywords

Harmonic mapping
Linearly connected domain
Second complex dilatation
Univalent

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10.1016/j.jmaa.2006.10.086

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title = "Univalent harmonic mappings and linearly connected domains",

abstract = "We investigate the relationship between the univalence of f and of h in the decomposition f = h + over(g, -) of a sense-preserving harmonic mapping defined in the unit disk D ⊂ C. Among other results, we determine the holomorphic univalent maps h for which there exists c > 0 such that every harmonic mapping of the form f = h + over(g, -) with | g′ | < c | h′ | is univalent. The notion of a linearly connected domain appears in our study in a relevant way.",

keywords = "Harmonic mapping, Linearly connected domain, Second complex dilatation, Univalent",

author = "M. Chuaqui and R. Hern{\'a}ndez",

note = "Funding Information: * Corresponding author. E-mail addresses: m.chuaqui@mat.puc.cl (M. Chuaqui), rodrigo.hernandez@uai.cl (R. Hern{\'a}ndez). 1 Work partially supported by Fondecyt Grant # 1030589.",

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AU - Hernández, R.

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N2 - We investigate the relationship between the univalence of f and of h in the decomposition f = h + over(g, -) of a sense-preserving harmonic mapping defined in the unit disk D ⊂ C. Among other results, we determine the holomorphic univalent maps h for which there exists c > 0 such that every harmonic mapping of the form f = h + over(g, -) with | g′ | < c | h′ | is univalent. The notion of a linearly connected domain appears in our study in a relevant way.

AB - We investigate the relationship between the univalence of f and of h in the decomposition f = h + over(g, -) of a sense-preserving harmonic mapping defined in the unit disk D ⊂ C. Among other results, we determine the holomorphic univalent maps h for which there exists c > 0 such that every harmonic mapping of the form f = h + over(g, -) with | g′ | < c | h′ | is univalent. The notion of a linearly connected domain appears in our study in a relevant way.

KW - Harmonic mapping

KW - Linearly connected domain

KW - Second complex dilatation

KW - Univalent

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SP - 1189

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JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

Univalent harmonic mappings and linearly connected domains

Abstract

Keywords

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