### Existence an regularity of constant mean curvature hypersurfaces in hyperbolic space.

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We study a singular perturbation problem arising in the scalar two-phase field model. Given a sequence of functions with a uniform bound on the surface energy, assume the Sobolev norms ${W}^{1,p}$ of the associated chemical potential fields are bounded uniformly, where $p\>\frac{n}{2}$ and $n$ is the dimension of the domain. We show that the limit interface as $\epsilon $ tends to zero is an integral varifold with a sharp integrability condition on the mean curvature.

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