TY - JOUR
T1 - Harmonic shears of slit and polygonal mappings
AU - Ponnusamy, Saminathan
AU - Quach, Tri
AU - Rasila, Antti
N1 - Funding Information:
This research was supported by a grant from the Jenny and Antti Wihuri Foundation.
PY - 2014/3/1
Y1 - 2014/3/1
N2 - In this paper, we study harmonic mappings by using the shear construction, introduced by Clunie and Sheil-Small in 1984. We consider two classes of conformal mappings, each of which maps the unit disk D univalently onto a domain which is convex in the horizontal direction, and shear these mappings with suitable dilatations ω. Mappings of the first class map the unit disk D onto four-slit domains and mappings of the second class take D onto regular n-gons. In addition, we discuss the minimal surfaces associated with such harmonic mappings. Furthermore, illustrations of mappings and associated minimal surfaces are given by using Mathematica.
AB - In this paper, we study harmonic mappings by using the shear construction, introduced by Clunie and Sheil-Small in 1984. We consider two classes of conformal mappings, each of which maps the unit disk D univalently onto a domain which is convex in the horizontal direction, and shear these mappings with suitable dilatations ω. Mappings of the first class map the unit disk D onto four-slit domains and mappings of the second class take D onto regular n-gons. In addition, we discuss the minimal surfaces associated with such harmonic mappings. Furthermore, illustrations of mappings and associated minimal surfaces are given by using Mathematica.
KW - Convex along real directions
KW - Convex functions
KW - Harmonic shear
KW - Harmonic univalent mappings
KW - Minimal surfaces
KW - Polygonal mappings
KW - Slit mappings
UR - http://www.scopus.com/inward/record.url?scp=84896443046&partnerID=8YFLogxK
U2 - 10.1016/j.amc.2014.01.076
DO - 10.1016/j.amc.2014.01.076
M3 - 文章
AN - SCOPUS:84896443046
VL - 233
SP - 588
EP - 598
JO - Applied Mathematics and Computation
JF - Applied Mathematics and Computation
SN - 0096-3003
ER -