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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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Volume 20, Issue 6 (Jan 2008)

Issues

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

Abstract

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.

About the article

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, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/FORUM.2008.047. Export Citation

Citing Articles

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[1]
Pham Hoang Ha, Le Bich Phuong, and Pham Duc Thoan
Topology and its Applications, 2016, Volume 199, Page 32
[2]
Pham Hoang Ha and Nguyen Van Trao
Journal of Mathematical Analysis and Applications, 2015, Volume 430, Number 1, Page 76
[3]
Yu Kawakami
Mathematische Zeitschrift, 2013, Volume 274, Number 3-4, Page 1249

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