Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2108.10022

Quasiconformal Extensions of Harmonic Univalent Mappings of the Unit Disk

Xiu-Shuang Ma
View original source ↗Read source document ↗Export metadata ↓

Abstract

This note examines sufficient conditions for the quasiconformal extendibility of harmonic mappings defined in the unit disk. It is demonstrated that a harmonic strongly starlike mapping admits a quasiconformal extension to the entire plane, and an explicit formulation of its extension function is provided. Additionally, the quasiconformal extendibility of harmonic mappings defined in the exterior of the unit disk is explored.

Explore related subjects

math.CV

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Xiu-Shuang Ma. 2025-08-30. Quasiconformal Extensions of Harmonic Univalent Mappings of the Unit Disk. https://arxiv.org/abs/2108.10022

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Uniform RC-positivity of tangent bundles

In this paper, we prove that every rationally connected projective manifold admits a smooth uniformly RC-positive Hermitian metric on its tangent bundle, answering Yang's question and giving a characterization of rational connectedness by uniform RC-positivity. We find an example to show that RC-positivity alone does not characterize rational connectedness. We also prove that uniform RC-positivity of the tangent bundle is preserved under blow-ups along connected smooth centers on compact complex manifolds. In the non-Kähler setting, we construct such metrics on all Hopf and Kato surfaces and obtain classification results for compact complex surfaces.

math.CV↗
arXiv2026

Growth, Distortion, and Schwarzian Norm Estimates for Exponentially Convex Functions

In this paper, we investigate the growth, distortion, pre-Schwarzian and Schwarzian norms of functions in the exponentially convex class \(\mathcal C_{e^λ}\), \(0<λ\leπ/2\), defined by \(1+zf''(z)/f'(z)\prec e^{λz}\). By representing the associated Schwarz function explicitly, we derive parameter-dependent estimates for \(f\), \(f'\), and the pre-Schwarzian derivative. We further obtain Schwarzian norm estimates under both the general normalization and the additional condition \(f''(0)=0\). The corresponding extremal problems are analyzed through suitable Schwarz functions, and the dependence of the resulting bounds on the exponential parameter is made explicit.

math.CV↗