Journal of the
Korean Mathematical Society JKMS

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 $f(x) + g(y)+ h(z) = 0$.

Keywords: Minimal surfaces, elliptic functions

MSC numbers: Primary 53A10; Secondary 53C42

Supported by: 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 grants-in-aid from JSPS Research Fellowships for Young Scientist (No. 21K13799).