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The Minimal Surfaces Over the Slanted Half-Planes, Vertical Strips and Single Slit

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Current Topics in Pure and Computational Complex Analysis

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Abstract

In this chapter, we discuss the minimal surfaces over the slanted half-planes, vertical strips, and single slit whose slit lies on the negative real axis. The representation of these minimal surfaces and the corresponding harmonic map**s are obtained explicitly. Finally, we illustrate the harmonic map**s of each of these cases together with their minimal surfaces pictorially with the help of mathematica. The content of this chapter is a shorter version of an article of the author’s report of 2011 and published in ar**v (http://arxiv.org/pdf/1204.2890.pdf) in 2012.

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Acknowledgements

The research of Liulan Li was supported by National Science Foundation (NSF) of China (No. 11201130), Hunan Provincial Natural Science Foundation of China (No. 14JJ1012) and construct program of the key discipline in Hunan province. Saminathan Ponnusamy is currently on leave from the Department of Mathematics, Indian Institute of Technology Madras, Chennai-600 036, India. The research of Matti Vuorinen was supported by the Academy of Finland, Project 2600066611. The authors thank the referee for useful comments.

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Authors and Affiliations

  1. Department of Mathematics and Computational Science, Hengyang Normal University, 421008, Hunan, Hengyang, People’s Republic of China

    Liulan Li

  2. Indian Statistical Institute (ISI) Chennai Centre, SETS (Society for Electronic Transactions and security), MGR Knowledge City, CIT Campus, Taramani, Chennai, 600113, India

    Saminathan Ponnusamy

  3. Department of Mathematics and Statistics, University of Turku, 20014, Turku, Finland

    Matti Vuorinen

Authors
  1. Liulan Li
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  2. Saminathan Ponnusamy
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  3. Matti Vuorinen
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Correspondence to Liulan Li .

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Editors and Affiliations

  1. Department of Mathematics, Walchand College of Engineering, Sangli, Maharashtra, India

    Santosh Joshi

  2. Department of Mathematics, Brigham Young University, Provo, Utah, USA

    Michael Dorff

  3. Department of Mathematics, University of Kalyani, Kalyani, West Bengal, India

    Indrajit Lahiri

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Li, L., Ponnusamy, S., Vuorinen, M. (2014). The Minimal Surfaces Over the Slanted Half-Planes, Vertical Strips and Single Slit. In: Joshi, S., Dorff, M., Lahiri, I. (eds) Current Topics in Pure and Computational Complex Analysis. Trends in Mathematics. Birkhäuser, New Delhi. https://doi.org/10.1007/978-81-322-2113-5_3

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