Periodic minimal surfaces
Periodic minimal surfaces
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周期性最小曲面
DOI：
10.1007/bf02566064
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发表时间：
1978
影响因子：
0.9
通讯作者：
B. Smyth
中科院分区：
文献类型：
--
作者：
T. Nagano;B. Smyth
对空间中三周期极小曲面的兴趣似乎可以追溯到HA Schwarz[11]的工作，从1865年第一个例子的构造开始(见w，我们已知的所有后续工作仅限于这些例子)。我们发现Neovius[14]的工作特别漂亮和有用。恰当地浸入空间的三周期极小曲面对应于紧定向曲面X到平面3-环面T的极小浸入f。有了诱导的共形结构，X是紧Riemann曲面，[是共形极小浸入。然后，我们的目标是研究平面3-环面中紧致黎曼曲面的共形极小浸没。这也是长野-史密斯[6，8]和米克斯[5]的观点。正确的设置是X和普适性的雅可比变化(见w扮演着不可或缺的角色。这里研究的主要问题是：
The interest in triply-periodic minimal surfaces in space seems to date from the work of HA Schwarz [11], beginning in 1865 with the construction of the first examples (see w All subsequent work known to us is restricted to these examples. We have found the work of Neovius [14] particularly beautiful and useful.A triply-periodic minimal surface properly immersed in space corresponds to a minimal immersion f of a compact oriented surface X into a fiat 3-torus T. With the induced conformal structure X is a compact Riemann surface and [is a conformal minimal immersion. Our object is then to study conformal minimal immersions of compact Riemann surfaces in fiat 3-tori. This is also the point of view of Nagano-Smyth [6, 8] and Meeks [5]. The correct setting for this is the Jacobi variety of X and universality (see w plays an indispensable role. The main question studied here is: