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Global bifurcation of solutions of the mean curvature spacelike equation in certain standard static spacetimes

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    * Corresponding author

The first author is supported by NNSF of China (No. 11871129) and Xinghai Youqing funds from Dalian University of Technology, the second one by Spanish MINECO Grant with FEDER funds MTM2016-78807-C2-1-P and the third author by Spanish MINECO Grant with FEDER funds MTM2017-82348-C2-1-P

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  • We study the existence/nonexistence and multiplicity of spacelike graphs for the following mean curvature equation in a standard static spacetime

    $ \begin{eqnarray} \text{div} \left(\frac{a\nabla u}{\sqrt{1-a^2\vert \nabla u\vert^2}}\right)+\frac{g(\nabla u, \nabla a)}{\sqrt{1-a^2\vert \nabla u\vert^2}} = \lambda NH \end{eqnarray} $

    with $ 0 $-Dirichlet boundary condition on the unit ball. According to the behavior of $ H $ near $ 0 $, we obtain the global structure of one-sign radial spacelike graphs for this problem. Moreover, we also obtain the existence and multiplicity of entire spacelike graphs.

    Mathematics Subject Classification: 35B32, 53A10.


    \begin{equation} \\ \end{equation}
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  • Figure 1.  Bifurcation diagrams of Theorem 1.1

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