TY - JOUR
T1 - Univalent harmonic mappings and linearly connected domains
AU - Chuaqui, M.
AU - Hernández, R.
N1 - Funding Information:
* Corresponding author. E-mail addresses: [email protected] (M. Chuaqui), [email protected] (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
SN - 0022-247X
VL - 332
SP - 1189
EP - 1194
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 2
ER -