发表机构
Universität Hamburg（汉堡大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过建立连续渐近平坦度量的坐标等周质量的新渐近表达式，证明了在弱正则性和非负分布标量曲率条件下，该质量具有坐标不变性并满足正质量定理，无需额外拓扑假设。
AI 中文摘要
将著名的黎曼正质量定理推广到低正则度度量是一个持续的努力，始于2000年代初，近年来重新引起了关注。与许多其他方法相反，我们既不想在无穷远处假设光滑性，也不想引入针对我们方法量身定制的新质量定义，而是回到由Huisken最初提出的坐标等周质量。我们建立了连续渐近平坦度量的坐标等周质量的新的渐近表达式，这构成了在合理假设下证明有限性准则、坐标不变性以及与Lee和LeFloch的广义ADM质量相等的主要成分。特别是，对于$W^{1,p}_{-\ au}$渐近平坦度量，其中$p>n$，$\ au>(n-2)/2$，且具有非负分布标量曲率，坐标等周质量确实是坐标不变的，并且我们在这种正则性下建立了正质量定理，除了渐近平坦性外没有任何拓扑假设。我们的证明依赖于类似于Lee、Lesourd和Unger的密度定理，但在更弱的正则性和衰减假设下，这可能具有独立的意义。
英文摘要
Extending the well-known Riemannian positive mass theorem to low-regularity metrics is an ongoing effort, starting from the early 2000s, that has recently seen renewed interest. Contrary to many other approaches we do not wish to assume smoothness at infinity nor to introduce a new definition of mass tailored to our approach, but rather go back to the coordinate isoperimetric mass originally proposed by Huisken. We establish new asymptotic expressions for the coordinate isoperimetric mass of continuous asymptotically flat metrics, which constitute the main ingredient in proving a finiteness criterion, coordinate invariance and equality to the generalized ADM mass of Lee and LeFloch under reasonable assumptions. In particular, for $W^{1,p}_{-τ}$ asymptotically flat metrics, with $p>n$, $τ>(n-2)/2$, and nonnegative distributional scalar curvature, the coordinate isoperimetric mass is indeed coordinate invariant, and we establish a positive mass theorem in this regularity without any topological assumptions aside from asymptotic flatness. Our proof relies on a density theorem similar to that of Lee, Lesourd, and Unger, but under a weaker regularity and decay assumption, which may be of independent interest.
Comments52 pages
