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- W4299550489 abstract "In this paper, we give some $C^{0}$ or $W^{1,p}$ limit theorems for total scalar curvatures. More precisely, we show that the lower bound of the total scalar curvatures on a closed manifold is preserved under the $W^{1, p}$ convergence of the Riemannian metrics for sufficiently large $p$ provided that each scalar curvature is nonnegative. Moreover, we give some counterexamples to this theorem on the Euclidean space. We also give a similar type of theorem for a sequence of metrics that converges to a metric only in the $C^{0}$ sense under some additional assumptions." @default.
- W4299550489 created "2022-10-02" @default.
- W4299550489 creator A5072966784 @default.
- W4299550489 date "2022-08-03" @default.
- W4299550489 modified "2023-10-18" @default.
- W4299550489 title "Limit theorems for the total scalar curvature" @default.
- W4299550489 doi "https://doi.org/10.48550/arxiv.2208.01865" @default.
- W4299550489 hasPublicationYear "2022" @default.
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