Separable minimal surfaces and their limit behavior
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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 $f(x) + g(y)+ h(z) = 0$.
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 $f(x) + g(y)+ h(z) = 0$.
참고문헌 (14)
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