Do Thi Thuy Hang, Si Duc Quang: On generalized Gauss maps of minimal surfaces sharing hypersurfaces in a projective variety, 61-78

Abstract:

In this article, we study the uniqueness problem for the generalized Gauss maps of minimal surfaces (with the same base) immersed in ${\Bbb R}^{n+1}$ which have the same inverse image of some hypersurfaces in a projective subvariety $V\subset{\mathbb{P}}^n({\Bbb C})$. As we know, this is the first time the unicity of generalized Gauss maps on minimal surfaces sharing hypersurfaces in a projective varieties is studied. Our results generalize and improve the previous results in this field.

Key Words: Gauss map, value distribution, holomorphic curve, uniqueness, algebraic dependence, hypersurface.

2020 Mathematics Subject Classification: Primary 53A10; Secondary 53C42.

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