论文标题
bartnik数据的非政策填充
Noncompact Fill-Ins of Bartnik Data
论文作者
论文摘要
我们通过考虑仅需要完整而不是紧凑而不是紧凑的非负标态曲率（NNSC）填充来概括Y. Shi和L.-F。\ tam的\ cite {shitam} brown-york质量的非阴性结果。此外，只要不完整是由具有正标性曲率的区域``屏蔽''的时间，甚至不需要完成NNSC填充填充物，并且发生足够远。 我们通过概括p。我们可以在紧凑的NNSC填充问题上类似地扩展其他结果，以允许完成（或屏蔽）NNSC填充。特别是，我们证明了miao〜 \ cite {miao20}定理的以下概括：在封闭的歧管$σ^{n-1} $上给出了任何公制$γ$，存在常数$λ$，因此对于任何完整（或屏蔽）nnsc填充$（或屏蔽）nnsc填充$（ω^n，g）$（ω^n，g）$（nnsc fill） $ \min_σh\leλ$，其中$ h $是相对于$ g $的$σ$的平均曲率。
We generalize Y. Shi and L.-F.\ Tam's \cite{ShiTam} nonnegativity result for the Brown-York mass, by considering nonnegative scalar curvature (NNSC) fill-ins that need only be complete rather than compact. Moreover, the NNSC fill-ins need not even be complete as long the incompleteness is ``shielded'' by a region with positive scalar curvature and occurs occurs sufficiently far away. We accomplish this by generalizing P.~Miao's~\cite{Miao02} positive mass theorem with corners to asymptotically flat manifolds that may have other complete ends, or possibly incomplete ends that are appropriately shielded. We can similarly extend other results on the compact NNSC fill-in problem to allow for complete (or shielded) NNSC fill-ins. In particular, we prove the following generalization of a theorem of Miao~\cite{Miao20}: Given any metric $γ$ on a closed manifold $Σ^{n-1}$, there exists a constant $λ$ such that for any complete (or shielded) NNSC fill-in $(Ω^n, g)$ of $(Σ^{n-1},γ)$, we have $\min_ΣH \le λ$, where $H$ is the mean curvature of $Σ$ with respect to $g$.
