Quasihyperbolic quasi-isometry and schwarz lemma of planar flat harmonic mappings

Qingtian Shi; Yi Qi

doi:10.2298/FIL1815371S

Quasihyperbolic quasi-isometry and schwarz lemma of planar flat harmonic mappings

Qingtian Shi^*
, Yi Qi

^*Corresponding author for this work

School of Mathematical Sciences

Beihang University

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

1 Scopus citations

Abstract

A sufficient condition of a flat harmonic quasiconformal mapping to be a quasihyperbolic quasi-isometry on any subdomain of C is given in this paper, which generalizes the corresponding results of Euclidean and 1/|ω| ² harmonic mappings. As an application, Schwarz lemma of flat harmonic mapping is also investigated. Besides, properties and constructions of flat harmonic mapping are obtained at the same time.

Original language	English
Pages (from-to)	5371-5383
Number of pages	13
Journal	Filomat
Volume	32
Issue number	15
DOIs	https://doi.org/10.2298/FIL1815371S
State	Published - 2018

Keywords

Euclidean harmonic mapping
Quasihyperbolic quasi-isometry
Quasiregular mapping
Schwarz lemma
ϕ-Harmonic quasiconformal mapping

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10.2298/FIL1815371S

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abstract = " A sufficient condition of a flat harmonic quasiconformal mapping to be a quasihyperbolic quasi-isometry on any subdomain of C is given in this paper, which generalizes the corresponding results of Euclidean and 1/|ω| 2 harmonic mappings. As an application, Schwarz lemma of flat harmonic mapping is also investigated. Besides, properties and constructions of flat harmonic mapping are obtained at the same time.",

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AU - Shi, Qingtian

AU - Qi, Yi

PY - 2018

Y1 - 2018

N2 - A sufficient condition of a flat harmonic quasiconformal mapping to be a quasihyperbolic quasi-isometry on any subdomain of C is given in this paper, which generalizes the corresponding results of Euclidean and 1/|ω| 2 harmonic mappings. As an application, Schwarz lemma of flat harmonic mapping is also investigated. Besides, properties and constructions of flat harmonic mapping are obtained at the same time.

AB - A sufficient condition of a flat harmonic quasiconformal mapping to be a quasihyperbolic quasi-isometry on any subdomain of C is given in this paper, which generalizes the corresponding results of Euclidean and 1/|ω| 2 harmonic mappings. As an application, Schwarz lemma of flat harmonic mapping is also investigated. Besides, properties and constructions of flat harmonic mapping are obtained at the same time.

KW - Euclidean harmonic mapping

KW - Quasihyperbolic quasi-isometry

KW - Quasiregular mapping

KW - Schwarz lemma

KW - ϕ-Harmonic quasiconformal mapping

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U2 - 10.2298/FIL1815371S

DO - 10.2298/FIL1815371S

M3 - 文章

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SN - 0354-5180

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SP - 5371

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JO - Filomat

JF - Filomat

IS - 15

ER -

Quasihyperbolic quasi-isometry and schwarz lemma of planar flat harmonic mappings

Abstract

Keywords

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