论文标题
密度和正质量定理，用于不完整的歧管
Density and positive mass theorems for incomplete manifolds
论文作者
论文摘要
对于具有渐近平坦端端的歧管，我们证明了一个密度定理，该密度定理在杰出的末端产生谐波渐近性，同时允许远离此端的不完整点（或负标态曲率）。我们使用它来改善正质量定理的“定量”版本（在尺寸$ 3 \ leq n \ leq 7 $）中，由最后两个带有S.-T的命名作者获得。 Yau [luy21]，在杰出的末端假设衰变更强。我们还基于MOT和$ $ $ bubbles之间的关系以及我们最近在带边界的时空正理定理方面的工作[llu21]，提供了该定理的替代证明。
For manifolds with a distinguished asymptotically flat end, we prove a density theorem which produces harmonic asymptotics on the distinguished end, while allowing for points of incompleteness (or negative scalar curvature) away from this end. We use this to improve the "quantitative" version of the positive mass theorem (in dimensions $3\leq n\leq 7$), obtained by the last two named authors with S.-T. Yau [LUY21], where stronger decay was assumed on the distinguished end. We also give an alternative proof of this theorem based on a relationship between MOTS and $μ$-bubbles and our recent work on the spacetime positive mass theorem with boundary [LLU21].
