论文标题
奇异的正质量定理与任意末端
Singular positive mass theorem with arbitrary ends
论文作者
论文摘要
由渐近平坦的流形的近期正面定理的最新进展和格罗莫夫对连续指标的标态曲率下限的定义的定义，我们启动了一个在正质量定理上，用于$ c^0 $ untunary entuny $ c^0。在这项工作中，我们建立了渐近平坦流形的正质量定理，$ c^0 $任意结束是指标为$ w^{1，p} _ {\ mathrm {\ mathrm {loc}} $，对于某些$ p \ in（n，\ infty] $，并且与非classection n in（n，\ infty] $相比， $ n- \ frac {p} {p-1} $。
Motivated by the recent progress on positive mass theorem for asymptotically flat manifolds with arbitrary ends and the Gromov's definition of scalar curvature lower bound for continuous metrics, we start a program on the positive mass theorem for asymptotically flat manifolds with $C^0$ arbitrary ends. In this work as the first step, we establish the positive mass theorem of asymptotically flat manifolds with $C^0$ arbitrary ends when the metric is $W^{1,p}_{\mathrm{loc}}$ for some $p\in(n,\infty]$ and is smooth away from a non-compact closed subset with Hausdorff dimension $n-\frac{p}{p-1}$. New techniques are developed to deal with non-compactness of the singular set.
