TY - JOUR

T1 - Univalent harmonic mappings and linearly connected domains

AU - Chuaqui, M.

AU - Hernández, R.

N1 - Funding Information:
* Corresponding author. E-mail addresses: m.chuaqui@mat.puc.cl (M. Chuaqui), rodrigo.hernandez@uai.cl (R. Hernández). 1 Work partially supported by Fondecyt Grant # 1030589.

PY - 2007/8/15

Y1 - 2007/8/15

N2 - We investigate the relationship between the univalence of f and of h in the decomposition f = h + over(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 + over(g, -) with | g′ | < c | h′ | is univalent. The notion of a linearly connected domain appears in our study in a relevant way.

AB - We investigate the relationship between the univalence of f and of h in the decomposition f = h + over(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 + over(g, -) with | g′ | < c | h′ | is univalent. The notion of a linearly connected domain appears in our study in a relevant way.

KW - Harmonic mapping

KW - Linearly connected domain

KW - Second complex dilatation

KW - Univalent

UR - http://www.scopus.com/inward/record.url?scp=34247337325&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2006.10.086

DO - 10.1016/j.jmaa.2006.10.086

M3 - Article

AN - SCOPUS:34247337325

VL - 332

SP - 1189

EP - 1194

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 2

ER -