Using the Lawson existence theorem of minimal surfaces and the symmetries of the Hopf fibration, we will construct symmetric embedded closed minimal surfaces in the three-dimensional sphere. These surfaces contain the Clifford torus, the Lawson’s minimal surfaces, and seven new minimal surfaces with genera 9, 25, 49, 121, 121, 361 and 841. We will also discuss the relation between such surfaces and the maximal extendable group actions on subsurfaces of the three-dimensional sphere.

中文翻译：

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具有高度对称性的三维球体中的最小曲面

利用最小曲面的Lawson存在定理和Hopf纤维的对称性，我们将在三维球体中构造对称的嵌入封闭最小曲面。这些曲面包含 Clifford 环面、Lawson 最小曲面和七个新的具有属的最小曲面9,25,49,121,121,361和841. 我们还将讨论这些表面与三维球体次表面上的最大可扩展群作用之间的关系。