TY - JOUR
T1 - Harmonic close-to-convex functions and minimal surfaces
AU - Ponnusamy, Saminathan
AU - Rasila, Antti
AU - Sairam Kaliraj, A.
N1 - Funding Information:
Research supported by the Jenny and Antti Wihuri Foundation. The third author thanks Council of Scientific and Industrial Research (CSIR), India, for providing financial support in the form of a Senior Research Fellowship to carry out this research.
PY - 2014/7
Y1 - 2014/7
N2 - In this paper, we study the family of sense-preserving complex-valued harmonic functions that are normalized close-to-convex functions on the open unit disk with. We derive a sufficient condition for to belong to the class. We take the analytic part of to be or and for a suitable choice of co-analytic part of, the second complex dilatation turns out to be a square of an analytic function. Hence, is lifted to a minimal surface expressed by an isothermal parameter. Explicit representation for classes of minimal surfaces are given. Graphs generated by using Mathematica are used for illustration.
AB - In this paper, we study the family of sense-preserving complex-valued harmonic functions that are normalized close-to-convex functions on the open unit disk with. We derive a sufficient condition for to belong to the class. We take the analytic part of to be or and for a suitable choice of co-analytic part of, the second complex dilatation turns out to be a square of an analytic function. Hence, is lifted to a minimal surface expressed by an isothermal parameter. Explicit representation for classes of minimal surfaces are given. Graphs generated by using Mathematica are used for illustration.
KW - Gaussian hypergeometric functions
KW - close-to-convex
KW - coefficient inequality
KW - convex in vertical direction
KW - minimal surfaces
KW - univalence
KW - univalent harmonic functions
UR - http://www.scopus.com/inward/record.url?scp=84898868572&partnerID=8YFLogxK
U2 - 10.1080/17476933.2013.800050
DO - 10.1080/17476933.2013.800050
M3 - 文章
AN - SCOPUS:84898868572
SN - 1747-6933
VL - 59
SP - 986
EP - 1002
JO - Complex Variables and Elliptic Equations
JF - Complex Variables and Elliptic Equations
IS - 7
ER -