Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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SEPARABLE MINIMAL SURFACES AND THEIR LIMIT BEHAVIOR

  • Daehwan Kim (Department of Mathematics Education Daegu University, School of Mathematics Korea Institute for Advanced Study) ;
  • Yuta Ogata (Department of Mathematics Faculty of Science Kyoto Sangyo University)
  • Received : 2023.09.24
  • Accepted : 2024.02.05
  • Published : 2024.07.01
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Abstract

A separable minimal surface is represented by the form of f(x) + g(y) + h(z) = 0, where f, g and h are real-valued functions of x, y and z, respectively. We provide exact equations for separable minimal surfaces with elliptic functions that are singly, doubly and triply periodic minimal surfaces and completely classify all them. In particular, parameters in the separable minimal surfaces change the shape of the surfaces, such as fundamental periods and its limit behavior, within the form f(x) + g(y) + h(z) = 0.

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Acknowledgement

The authors would like to thank their advisors Juncheol Pyo andWayne Rossman. We also warmly thank the referees for their careful reading of our paper and giving us valuable comments. The first author was supported by the National Research Foundation of Korea (NRF) grants funded by the Korea government (MSIT) (No. NRF-2019R1C1C1004819 and No. NRF-2022R1H1A2091877). The second author was supported by a grantsinaid from JSPS Research Fellowships for Young Scientist (No. 21K13799).

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