Abstract
In this work, we consider sequences of \(C^2\) metrics which converges to a \(C^2\) metric in \(C^0\) sense. We show that if the scalar curvature of the sequence is almost non-negative in the integral sense, then the limiting metric has scalar curvature lower bound in point-wise sense.
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Acknowledgements
The authors would like to thank Professor Richard Bamler for his interest in this note and helpful discussions. The authors would like to thank the referee for useful comments.
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Huang, Y., Lee, MC. Scalar curvature lower bound under integral convergence. Math. Z. 303, 2 (2023). https://doi.org/10.1007/s00209-022-03155-9
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DOI: https://doi.org/10.1007/s00209-022-03155-9