Topological structure of the pre-Schwarzian derivative space of harmonic mappings

Tao Cheng; Yan Wu; Haoran Zou

doi:10.1016/j.jmaa.2026.130402

Topological structure of the pre-Schwarzian derivative space of harmonic mappings

Tao Cheng
, Yan Wu
, Haoran Zou^*

^*Corresponding author for this work

School of Mathematical Sciences

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

Abstract

We construct the pre-Schwarzian derivative space H of harmonic mappings and investigate its topological connectedness. Furthermore, we show that the interior of H contains the model of the universal Teichmüller space embedded by pre-Schwarzian derivative.

Original language	English
Article number	130402
Journal	Journal of Mathematical Analysis and Applications
Volume	559
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2026.130402
State	Published - 1 Jul 2026

Keywords

Harmonic mapping
Pre-Schwarzian derivative
Quasiconformal extension
Universal Teichmüller space

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10.1016/j.jmaa.2026.130402

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title = "Topological structure of the pre-Schwarzian derivative space of harmonic mappings",

abstract = "We construct the pre-Schwarzian derivative space H of harmonic mappings and investigate its topological connectedness. Furthermore, we show that the interior of H contains the model of the universal Teichm{\"u}ller space embedded by pre-Schwarzian derivative.",

keywords = "Harmonic mapping, Pre-Schwarzian derivative, Quasiconformal extension, Universal Teichm{\"u}ller space",

author = "Tao Cheng and Yan Wu and Haoran Zou",

note = "Publisher Copyright: {\textcopyright} 2026 Elsevier Inc.",

year = "2026",

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doi = "10.1016/j.jmaa.2026.130402",

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T1 - Topological structure of the pre-Schwarzian derivative space of harmonic mappings

AU - Cheng, Tao

AU - Wu, Yan

AU - Zou, Haoran

PY - 2026/7/1

Y1 - 2026/7/1

N2 - We construct the pre-Schwarzian derivative space H of harmonic mappings and investigate its topological connectedness. Furthermore, we show that the interior of H contains the model of the universal Teichmüller space embedded by pre-Schwarzian derivative.

AB - We construct the pre-Schwarzian derivative space H of harmonic mappings and investigate its topological connectedness. Furthermore, we show that the interior of H contains the model of the universal Teichmüller space embedded by pre-Schwarzian derivative.

KW - Harmonic mapping

KW - Pre-Schwarzian derivative

KW - Quasiconformal extension

KW - Universal Teichmüller space

UR - https://www.scopus.com/pages/publications/105027541291

U2 - 10.1016/j.jmaa.2026.130402

DO - 10.1016/j.jmaa.2026.130402

M3 - 文章

AN - SCOPUS:105027541291

SN - 0022-247X

VL - 559

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

M1 - 130402

ER -

Topological structure of the pre-Schwarzian derivative space of harmonic mappings

Abstract

Keywords

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