AI 中文总结
本文构造了一序列Kähler度量，其ADM质量趋于零但不收敛于欧几里得空间，证明Klemmensen稳定性结果中切除条件的必要性。
AI 中文摘要
我们在C^2上构造了一序列具有非负且可积标量曲率的AE Kähler度量，其ADM质量趋于零，但对于合适的基点选择，该序列在尖点Gromov-Hausdorff意义下不收敛于欧几里得空间。这表明，在没有额外假设的情况下，Klemmensen关于Kähler流形正质量定理稳定性结果中的切除是至关重要的，这与（三维）黎曼情形中的发现一致。
英文摘要
We construct a sequence of AE Kähler metrics on C^2 with nonnegative and integrable scalar curvature whose ADM mass tends to zero but which, for a suitable choice of basepoints, fails to converge to Euclidean space in the pointed Gromov-Hausdorff sense. This shows that, without any additional assumptions, the excision in Klemmensen's stability result for the positive mass theorem for Kähler manifolds is crucial, which aligns with the findings in the (3-dimensional) Riemannian case.
Comments21 pages
