Harmonic mappings, univalence criteria and a theorem of Lehtinen

Iason Efraimidis; Rodrigo Hernández

doi:10.1007/s41478-026-01157-y

Harmonic mappings, univalence criteria and a theorem of Lehtinen

Iason Efraimidis
, Rodrigo Hernández

Faculty of Engineering and Science

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

Abstract

The harmonic inner radius of a planar domain is the largest constant with which a univalence criterion via the Schwarzian derivative holds for harmonic mappings. We show that for the unit disk and for every domain that omits an open set. This is an analogue of a theorem of Lehtinen in the setting of holomorphic functions. We provide two related univalence criteria for harmonic mappings.

Original language	English
Journal	Journal of Analysis
DOIs	https://doi.org/10.1007/s41478-026-01157-y
State	Accepted/In press - 2026

Keywords

Harmonic mappings
Schwarzian derivative
Univalence criteria

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10.1007/s41478-026-01157-y

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title = "Harmonic mappings, univalence criteria and a theorem of Lehtinen",

abstract = "The harmonic inner radius of a planar domain is the largest constant with which a univalence criterion via the Schwarzian derivative holds for harmonic mappings. We show that for the unit disk and for every domain that omits an open set. This is an analogue of a theorem of Lehtinen in the setting of holomorphic functions. We provide two related univalence criteria for harmonic mappings.",

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language = "English",

journal = "Journal of Analysis",

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AU - Efraimidis, Iason

AU - Hernández, Rodrigo

N1 - Publisher Copyright: © The Author(s) 2026.

PY - 2026

Y1 - 2026

N2 - The harmonic inner radius of a planar domain is the largest constant with which a univalence criterion via the Schwarzian derivative holds for harmonic mappings. We show that for the unit disk and for every domain that omits an open set. This is an analogue of a theorem of Lehtinen in the setting of holomorphic functions. We provide two related univalence criteria for harmonic mappings.

AB - The harmonic inner radius of a planar domain is the largest constant with which a univalence criterion via the Schwarzian derivative holds for harmonic mappings. We show that for the unit disk and for every domain that omits an open set. This is an analogue of a theorem of Lehtinen in the setting of holomorphic functions. We provide two related univalence criteria for harmonic mappings.

KW - Harmonic mappings

KW - Schwarzian derivative

KW - Univalence criteria

UR - https://www.scopus.com/pages/publications/105045252814

U2 - 10.1007/s41478-026-01157-y

DO - 10.1007/s41478-026-01157-y

M3 - Article

AN - SCOPUS:105045252814

SN - 0971-3611

JO - Journal of Analysis

JF - Journal of Analysis

ER -

Harmonic mappings, univalence criteria and a theorem of Lehtinen

Abstract

Keywords

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