A Parametrical Representation of the Riemann''s Minimal Surface with the Weierstrass Functions
碩士 === 國立臺灣大學 === 數學研究所 === 91 === Since every minimal surface in R^3 has an unique Weierstrass Representation, we can define the minimal surface by giving it''s Weierstrass data. In 1997, Gray gave a parametrical reprensentation of Costa''s minimal surface. In this pa...
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| Format: | Others |
| Language: | en_US |
| Published: |
2003
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| Online Access: | http://ndltd.ncl.edu.tw/handle/30562754536634177649 |
| Summary: | 碩士 === 國立臺灣大學 === 數學研究所 === 91 === Since every minimal surface in R^3 has an unique Weierstrass
Representation, we can define the minimal surface by giving it''s Weierstrass data. In 1997, Gray gave a parametrical reprensentation of Costa''s minimal surface. In this paper, we try to imitate Gray''s formula for Costa''s minimal surface and give a similar formulas to another famous embedded minimal surface : the Riemann''s minimal surface S0, and to an immersed minimal surface S1. All these three surfaces have Weierstrass data involving the Weierstrass p-function and the Weierstrass Zeta function. This similarity gives us a thought to extend Gray''s result on Costa''s case to S0 and S1.
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