Abstract:In this note we show that a closed Riemannian manifold does not admit a fill-in with nonnegative scalar curvature if the mean curvature is point-wise large. Similar result also holds for fill-ins with a negative scalar curvature lower bound.

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中文翻译：

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具有大平均曲率的NNSC填充不存在

摘要：在此注释中，我们表明，如果平均曲率是逐点大的，则封闭的黎曼流形不接受具有非负标量曲率的填充。对于具有负标量曲率下限的填充，也具有类似的结果。

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