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The Mean Curvature Type Flow in Lorentzian Warped Product

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Abstract

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.

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Acknowledgments

The authors would like to thank the referees for their valuable comments and suggestions, which allowed them to improve this paper.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, China

    Guanghan Li & Kuicheng Ma

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  1. Guanghan Li
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  2. Kuicheng Ma
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Correspondence to Kuicheng Ma.

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This work is supported in part by NSFC (No. 11761080 and No. 11871053).

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Li, G., Ma, K. The Mean Curvature Type Flow in Lorentzian Warped Product. Math Phys Anal Geom 23, 15 (2020). https://doi.org/10.1007/s11040-020-09338-2

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  • DOI: https://doi.org/10.1007/s11040-020-09338-2

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