作　　者： ; ;

机构地区： 西北工业大学自动化学院

出　　处： 《浙江大学学报（理学版）》 2003年第6期612-616,共5页

摘　　要： Hoffman和Meeks采用增加R3中嵌入极小的Costa曲面的亏格和端点处的法向旋转对称阶数的技巧,构造了R3中一族具有任意高亏格的嵌入极小曲面.借鉴这种思想,通过选择适当的Weierstrass表示对,在端点法向非对称旋转的构造方式下,将两个都仅有一个Enneper型端,全曲率分别为-8π和-12π,亏格为1和2的Chen-Gacksta¨tter曲面分别推广为一族都仅有一个多重数的端,全曲率分别为-8kπ和-12kπ(k∈Z+)的多个亏格的完备的浸入极小曲面.证明了这两类完备浸入极小曲面的存在性. The technique of increasing the genus and symmetry to construct new embedded minimal surfaces in R^3 with arbitrary high genus, was established by Hoffman and Meeks. Triggered by this idea, using the construction of increasing nonsymmetric winding orders of the end and looking for the proper Weierstrass representation pairs, it was generalized that the Chen-Gackst(a)¨tter surfaces, both having only one Enneper type end, with total curvatures -8π and -12π, to a family of complete immersed minimal sufaces with total curvatures -8kπ and -12kπ (k∈Z^+) respectively, of higher genus. All the new examples have only one end with high multiplicity. Finally, the existence of immersed minimal surfaces was proven. For k=1, the constructions lead to original Chen-Gackst(a)¨tter surfaces.

关 键 词： 完备极小曲面 有限全曲率 超椭圆函数 浸入端 亏格 欧氏空间

领　　域： [理学] [理学]