The rigidity of the Riemannian positive mass theorem for asymptotically hyperbolic manifolds states that the total mass of such a manifold is zero if and only if the manifold is isometric to the hyperbolic space. This leads to study the stability of this statement, that is, if the total mass of an asymptotically hyperbolic manifold is almost zero, is this manifold close to the hyperbolic space in any way? Motivated by the work of Huang, Lee and Sormani for asymptotically flat graphical manifolds with respect to intrinsic flat distance, we show the intrinsic flat stability of the positive mass theorem for a class of asymptotically hyperbolic graphical manifolds by adapting the positive answer to this question provided by Huang, Lee and the third named author.

渐近双曲流形的黎曼正质量定理的刚性表明，当且仅当流形与双曲空间等距时，这种流形的总质量为零。这就引出了研究这个说法的稳定性，即如果一个渐近双曲流形的总质量几乎为零，那么这个流形是否有任何方式接近双曲空间？受 Huang、Lee 和 Sormani 关于内在平坦距离的渐近平坦图流形工作的启发，我们通过调整所提供的该问题的正答案，展示了一类渐近双曲图流形的正质量定理的内在平坦稳定性由黄、李和第三位署名作者撰写。