Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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ON SPIRALLIKE FUNCTIONS RELATED TO BOUNDED RADIUS ROTATION

  • Cetinkaya, Asena (Department of Mathematics and Computer Science Istanbul Kultur University) ;
  • Tastan, Hakan Mete (Department of Mathematics, Faculty of Science, Istanbul University)
  • Received : 2021.09.25
  • Accepted : 2021.11.10
  • Published : 2022.03.25
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Abstract

In the present paper, we prove the growth and distortion theorems for the spirallike functions class 𝓢k(λ) related to boundary radius rotation, and by using the distortion result, we get an estimate for the Gaussian curvature of a minimal surface lifted by a harmonic function whose analytic part belongs to the class 𝓢k(λ). Moreover, we determine and draw the minimal surface corresponding to the harmonic Koebe function.

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Acknowledgement

We would like to thank Professor Bahar KIRIK RACZ for her contribution to the drawing of the minimal surface in Figure 1 using the Maple program.

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