Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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MINIMAL SURFACE SYSTEM IN EUCLIDEAN FOUR-SPACE

  • Hojoo Lee (Department of Mathematics and Institute of Pure and Applied Mathematics Jeonbuk National University)
  • Received : 2022.03.02
  • Accepted : 2022.10.27
  • Published : 2023.01.01
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Abstract

We construct generalized Cauchy-Riemann equations of the first order for a pair of two ℝ-valued functions to deform a minimal graph in ℝ3 to the one parameter family of the two dimensional minimal graphs in ℝ4. We construct the two parameter family of minimal graphs in ℝ4, which include catenoids, helicoids, planes in ℝ3, and complex logarithmic graphs in ℂ2. We present higher codimensional generalizations of Scherk's periodic minimal surfaces.

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References

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