Given a complete hypersurface isometrically immersed in an ambient manifold, in this paper we provide a lower bound for the norm of the mean curvature vector field of the immersion assuming that: 1) The ambient manifold admits a Killing submersion with unit-length Killing vector field. 2)The projection of the image of the immersion is bounded in the base manifold. 3)The hypersurface is stochastically complete, or the immersion is proper.

中文翻译：

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Killing submersions 中超曲面的平均曲率与有界阴影

给定一个完全浸入环境流形中的完整超曲面，在本文中，我们提供浸入式平均曲率矢量场范数的下界，假设：1) 环境流形允许具有单位长度 Killing 矢量场的 Killing 浸没. 2）浸入图像的投影在基流形中是有界的。3）超曲面是随机完备的，或者浸入是适当的。