Construction Of Minimal Surfaces In R～3 With Higher Winding Order Ends

The object of the paper is a kind of complete minimal surfaces in R³, which have finite total curvature and special type end. We started from a special type minimal surface called M₂, which has 0 genus and two ends, and both of the ends have winding order 2. After calculate the W-data of M_n{1≤ n ≤5), we gave the W—data of M_n(n > 0), and then proved it. In order to analysis the properties of M_n, we designed a program package using Java, which is applicable to general minimal surfaces, to draw the image of M_n. Based on the analysis, we discussed the symmetric property for special parameters.Chapter 1 introduces the history, development and application of minimal surfaces. Finally, we introduced the application of Computer technology in minimal surfaces.Chapter 2 introduces the equation of minimal surfaces and Weierstrass Representation Theorem. And then introduces Gauss map of minimal surfaces. Finally, we introduced some classical minimal surfaces.Chapter 3 introduces the theory of minimal surfaces with finite total curvature, including uniqueness results and existing construction methods.Chapter 4 is the main work of the paper, we got the following result:There exists a family of complete oriented minimal surfaces in R3 with finite total curvature —AnÏ€, each of which has 0 genus and two ends, and both of the ends have winding order n, where n = 1,2,3,...Chapter 5 introduces the basic methods of drawing minimal surfaces. Chapter 6 includes conclusion.