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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Brüdern, Jörg / Cohen, Frederick R. / Droste, Manfred / Duzaar, Frank / Neeb, Karl-Hermann / Noguchi, Junjiro / Shahidi, Freydoon / Sogge, Christopher D. / Wienhard, Anna

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The Gauss map of pseudo-algebraic minimal surfaces

Yu Kawakami / Ryoichi Kobayashi / Reiko Miyaoka
Published Online: 2008-12-15 | DOI: https://doi.org/10.1515/FORUM.2008.047


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.

Received: 2006-04-12

Revised: 2007-02-26

Revised: 2007-03-22

Accepted: 2007-05-09

Published Online: 2008-12-15

Published in Print: 2008-11-01

Citation Information: Forum Mathematicum. Volume 20, Issue 6, Pages 1055–1069, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/FORUM.2008.047, December 2008

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