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A Bernstein type theorem for minimal hypersurfaces via Gauss maps
Journal of Functional Analysis ( IF 1.7 ) Pub Date : 2020-06-01 , DOI: 10.1016/j.jfa.2020.108469
Qi Ding

Let $M$ be an $n$-dimensional smooth oriented complete minimal hypersurface in $\mathbb{R}^{n+1}$ with Euclidean volume growth. We show that if the image under the Gauss map of $M$ avoids some neighborhood of a half-equator, then $M$ must be an affine hyperplane.

中文翻译:

基于高斯图的最小超曲面的伯恩斯坦型定理

令 $M$ 是 $\mathbb{R}^{n+1}$ 中的 $n$ 维光滑定向完全最小超曲面,具有欧几里德体积增长。我们证明,如果 $M$ 的高斯图下的图像避开了半赤道的某个邻域,则 $M$ 必须是仿射超平面。
更新日期:2020-06-01
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