Conformal tori with almost non-negative scalar curvature
Conformal tori with almost non-negative scalar curvature
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DOI：
10.1007/s00526-022-02220-9
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发表时间：
2022-04
影响因子：
2.1
通讯作者：
Jianchun Chu;Man-Chun Lee
中科院分区：
文献类型：
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作者：
Jianchun Chu;Man-Chun Lee
本文研究了环面上几乎非负数量曲率的度量序列。我们证明了如果该序列一致共形于另一个具有有界Ricci几何的度量序列，则它在保体积的内禀平坦意义、测量Gromov-Hausdorff意义和测量意义下收敛于平坦度量.此外，在具有非正Yamabe不变量的流形上也有类似的稳定性。
In this work, we consider sequence of metrics with almost non-negative scalar curvature on torus. We show that if the sequence is uniformly conformal to another sequence of metrics with bounded Ricci geometry, then it converges to a flat metric in the volume preserving intrinsic flat sense, the measured Gromov–Hausdorff sense andsense. Moreover, similar stability also holds on manifolds with non-positive Yamabe invariant.