Univalent harmonic mappings and linearly connected domains

By Martin Chuaqui, R. Hernández. 2007

49 citations recorded by the source corpus.

Abstract We investigate the relationship between the univalence of f and of h in the decomposition f = h + g ¯ of a sense-preserving harmonic mapping defined in the unit disk D ⊂ C . Among other results, we determine the holomorphic univalent maps h for which there exists c > 0 such that every harmonic mapping of the form f = h + g ¯ with | g ′ | c | h ′ | is univalent. The notion of a linearly connected domain appears in our study in a relevant way.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/441e6cada94286da39fe3685a9d73a8a4d3ccb25

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In Applied Mathematics

1. Saminathan Ponnusamy
2. Xiantao Wang
3. Shaolin Chen
4. Ilgiz R. Kayumov
5. A. Ismagilov
6. Zhihong Liu
7. V. Allu
8. H. Halder

In Geometry and Topology

1. Saminathan Ponnusamy
2. Xiantao Wang
3. Shaolin Chen
4. 'Arp'ad Baricz
5. V. Allu
6. H. Halder

Citations in the corpus

• Properties of Some Classes of Planar Harmonic and Planar Biharmonic Mappings (2011, background): “In a recent paper, Chuaqui and Hernández [4] investigated the relationship between the univalency of planar harmonic mappings f and the linear connectivity of f (D), see for example [4, Theorem 1].”