论文标题
$ l^p $ - 稳定性和正标性曲率刚度
$L^p$-stability and positive scalar curvature rigidity of Ricci-flat ALE manifolds
论文作者
论文摘要
我们证明，对于$ l^p \ cap l^\ int（1，n）$中的任何$ p \ in（1，n）$，$ n $是$ n $是折叠的尺寸。特别是，我们的结果适用于所有已知的$ 4 $维式引力Instantons的示例。我们的衰减率足以证明$ l^p $中的正标度曲率刚度，对于\ left [1，\ frac {n} {n-2} \ right）$的每个$ p \ in \ ews p $ p $ c。
We prove stability of integrable ALE manifolds with a parallel spinor under Ricci flow, given an initial metric which is close in $L^p \cap L^\infty$, for any $p \in (1, n)$, where $n$ is the dimension of the manifold. In particular, our result applies to all known examples of $4$-dimensional gravitational instantons. Our decay rates are strong enough to prove positive scalar curvature rigidity in $L^p$, for each $p \in \left[1, \frac{n}{n-2}\right)$, generalizing a result by Appleton.
