J. Korean Math. Soc. 2023; 60(1): 71-90
Online first article December 13, 2022 Printed January 1, 2023
https://doi.org/10.4134/JKMS.j220095
Copyright © The Korean Mathematical Society.
Hojoo Lee
Jeonbuk National University
We construct generalized Cauchy-Riemann equations of the first order for a pair of two $\mathbb{R}$-valued functions to deform a minimal graph in ${\mathbb{R}}^{3}$ to the one parameter family of the two dimensional minimal graphs in ${\mathbb{R}}^{4}$. We construct the two parameter family of minimal graphs in ${\mathbb{R}}^{4}$, which include catenoids, helicoids, planes in ${\mathbb{R}}^{3}$, and complex logarithmic graphs in ${\mathbb{C}}^{2}$. We present higher codimensional generalizations of Scherk's periodic minimal surfaces.
Keywords: Minimal surface system, Gauss map, Scherk surface
MSC numbers: Primary 53A10, 49Q05
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