In this article, we study the mean curvature type flow of spacelike graphical hypersurfaces in Lorentzian warped product. This flow was introduced by Guan and Li in [ 6 ]. Under mild assumptions on the warping function and the Ricci curvature of the base manifold, we obtain the longtime existence and smooth convergence to an umbilic slice for this flow in Lorentzian setting. As an application of the convergence result, we obtain an inequality between the enclosed volume and the area of the graphical solution to our flow.

中文翻译：

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洛伦兹翘曲产品中的平均曲率型流动

在本文中，我们研究了洛伦兹翘曲积中类空间图形超曲面的平均曲率型流。这个流程是由 Guan 和 Li 在 [6] 中介绍的。在对翘曲函数和基流形的 Ricci 曲率的温和假设下，我们在洛伦兹设置中获得了这种流动的长期存在和平滑收敛到脐带切片。作为收敛结果的应用，我们获得了封闭体积与我们的流动的图形解的面积之间的不等式。