Harmonic close-to-convex functions and minimal surfaces

Saminathan Ponnusamy; Antti Rasila; A. Sairam Kaliraj

doi:10.1080/17476933.2013.800050

Harmonic close-to-convex functions and minimal surfaces

Saminathan Ponnusamy, Antti Rasila^*, A. Sairam Kaliraj

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	986-1002
Number of pages	17
Journal	Complex Variables and Elliptic Equations
Volume	59
Issue number	7
DOIs	https://doi.org/10.1080/17476933.2013.800050
State	Published - Jul 2014
Externally published	Yes

Keywords

Gaussian hypergeometric functions
close-to-convex
coefficient inequality
convex in vertical direction
minimal surfaces
univalence
univalent harmonic functions

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10.1080/17476933.2013.800050

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title = "Harmonic close-to-convex functions and minimal surfaces",

abstract = "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.",

keywords = "Gaussian hypergeometric functions, close-to-convex, coefficient inequality, convex in vertical direction, minimal surfaces, univalence, univalent harmonic functions",

author = "Saminathan Ponnusamy and Antti Rasila and {Sairam Kaliraj}, A.",

note = "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.",

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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

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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 -

Harmonic close-to-convex functions and minimal surfaces

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Keywords

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