Boundary Schwarz Lemma for Harmonic Mappings Having Zero of Order p

Xiao Jin Bai; Jie Huang; Jian Feng Zhu

doi:10.1007/s40840-020-00980-1

Boundary Schwarz Lemma for Harmonic Mappings Having Zero of Order p

Xiao Jin Bai, Jie Huang, Jian Feng Zhu

Mathematics with Computer Science

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

Abstract

Suppose w is a sense-preserving harmonic mapping of the unit disk D such that w(D) ⊆ D and w has a zero of order p ≥ 1 at z = 0. In this paper, we first improve the Schwarz lemma for w, and then, we establish its boundary Schwarz lemma. Moreover, by using the automorphism of D, we further generalize this result.

MSC Codes 30C15(Primary), 31A20, 30C62(Secondary)

Original language	English
Pages (from-to)	827-838
Number of pages	12
Journal	Bulletin of the Malaysian Mathematical Sciences Society
Volume	44
Issue number	2
DOIs	https://doi.org/10.1007/s40840-020-00980-1
State	Published - 24 Jul 2020

Keywords

Boundary Schwarz lemma
Harmonic mappings
Multiplicity of zeros
Schwarz lemma

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abstract = "Suppose w is a sense-preserving harmonic mapping of the unit disk D such that w(D) ⊆ D and w has a zero of order p ≥ 1 at z = 0. In this paper, we first improve the Schwarz lemma for w, and then, we establish its boundary Schwarz lemma. Moreover, by using the automorphism of D, we further generalize this result.MSC Codes 30C15(Primary), 31A20, 30C62(Secondary)",

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AU - Huang, Jie

AU - Zhu, Jian Feng

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N2 - Suppose w is a sense-preserving harmonic mapping of the unit disk D such that w(D) ⊆ D and w has a zero of order p ≥ 1 at z = 0. In this paper, we first improve the Schwarz lemma for w, and then, we establish its boundary Schwarz lemma. Moreover, by using the automorphism of D, we further generalize this result.MSC Codes 30C15(Primary), 31A20, 30C62(Secondary)

AB - Suppose w is a sense-preserving harmonic mapping of the unit disk D such that w(D) ⊆ D and w has a zero of order p ≥ 1 at z = 0. In this paper, we first improve the Schwarz lemma for w, and then, we establish its boundary Schwarz lemma. Moreover, by using the automorphism of D, we further generalize this result.MSC Codes 30C15(Primary), 31A20, 30C62(Secondary)

KW - Boundary Schwarz lemma

KW - Harmonic mappings

KW - Multiplicity of zeros

KW - Schwarz lemma

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JO - Bulletin of the Malaysian Mathematical Sciences Society

JF - Bulletin of the Malaysian Mathematical Sciences Society

IS - 2

ER -

Boundary Schwarz Lemma for Harmonic Mappings Having Zero of Order p

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