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The Gauss map of pseudo-algebraic minimal surfaces
1Graduate school of Mathematics, Nagoya University, Nagoya, 464-8602/Japan. (email)
2Graduate school of Mathematics, Nagoya University, Nagoya, 464-8602/Japan. (email)
3Mathematical Institute, Tohoku University, Sendai, 980-8578/Japan. (email)
Citation Information: Forum Mathematicum. Volume 20, Issue 6, Pages 1055–1069, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: 10.1515/FORUM.2008.047, December 2008
- Published Online:
We refine Osserman's argument on the exceptional values of the Gauss map of algebraic minimal surfaces. This gives an effective estimate for the number of exceptional values and the totally ramified value number for a wider class of complete minimal surfaces that includes algebraic minimal surfaces. It also provides a new proof of Fujimoto's theorem for this class, which not only simplifies the proof but also reveals the geometric meaning behind it.
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