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arXiv · 1411.3037

The Gauss map and total curvature of complete minimal Lagrangian surfaces in the complex two-space

Reiko Aiyama·Kazuo Akutagawa·Yu Kawakami
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Abstract

The purpose of this paper is to reveal the relationship between the total curvature and the global behavior of the Gauss map of a complete minimal Lagrangian surface in the complex two-space. To achieve this purpose, we show the precise maximal number of exceptional values of the Gauss map for a complete minimal Lagrangian surface with finite total curvature in the complex two-space. Moreover, we prove that if the Gauss map of a complete minimal Lagrangian surface which is not a Lagrangian plane omits three values, then it takes all other values infinitely many times.

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Reiko Aiyama, Kazuo Akutagawa, Yu Kawakami. 2015-01-30. The Gauss map and total curvature of complete minimal Lagrangian surfaces in the complex two-space. https://arxiv.org/abs/1411.3037

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