标题： Green函数与渐近双曲$3$-流形的正质量定理 显示英文标题

标题： Green functions and a positive mass theorem for asymptotically hyperbolic $3$-manifolds

摘要： 我们证明了一个新的正质量定理，适用于渐近双曲型的三维流形，其阶数大于$1$。 所考虑的质量量是 Dahl、McCormick 和第一作者在一篇论文中最近引入的体积重整化质量。 证明基于 Laplace 算子在任意点为中心的 Green 函数沿其水平集的单调性公式。 为了使该论证成立，我们要求流形的第二同调群中不包含任何球面类。 显示英文摘要

摘要： We prove a new positive mass theorem for three-dimensional manifolds which are asymptotically hyperboloidal of order greater than $1$. The mass quantity under consideration is the volume-renormalized mass recently introduced in a paper by Dahl, McCormick and the first author. The proof is based on a monotonicity formula holding along the level sets of the Green function for the Laplace operator centered at an arbitrary point. In order for this argument to work out, we require that the second homology of the manifold does not contain any spherical classes.