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

  • Liulan Li
  • Saminathan Ponnusamy
  • Matti Vuorinen
Part of the Trends in Mathematics book series (TM)


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 mappings are obtained explicitly. Finally, we illustrate the harmonic mappings 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 arXiv ( in 2012.


Harmonic Mapping Minimal Surface Blaschke Product Vertical Strip Strip Domain 
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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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Copyright information

© Springer India 2014

Authors and Affiliations

  • Liulan Li
    • 1
  • Saminathan Ponnusamy
    • 2
  • Matti Vuorinen
    • 3
  1. 1.Department of Mathematics and Computational ScienceHengyang Normal UniversityHunanPeople’s Republic of China
  2. 2.Indian Statistical Institute (ISI) Chennai CentreSETS (Society for Electronic Transactions and security)ChennaiIndia
  3. 3.Department of Mathematics and StatisticsUniversity of TurkuTurkuFinland

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