论文标题
限制总标率曲率定理
Limit theorems for the total scalar curvature
论文作者
论文摘要
在本文中，我们给出了一些$ W^{1，p} $限制总标度曲率的定理。更准确地说，我们表明，封闭的歧管上总标量曲率的下限保留在$ W^{1，p} $融合的Riemannian指标的融合下，只要每个标量曲率都是非校验的，则足够大的$ p $。我们还为一系列指标提供了类似类型的定理，该指标仅在$ c^{0} $中收敛到指标。此外，我们在欧几里得空间上对该定理进行了一些反例。
In this paper, we give some $W^{1,p}$ limit theorems for the total scalar curvature. 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. 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. Moreover, we give some counterexamples to this theorem on the Euclidean space.
