Convergence of the Ricci flow to Ricci-flat ALE manifolds and positive scalar curvature rigidity

Abstract

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.

99 pages, published version

References in corpus (3)

• Stability and instability of Ricci solitons
• Stability of Einstein metrics under Ricci flow
• Stability of ALE Ricci-flat manifolds under Ricci flow

Cited by in corpus (1)

• Spectra, rigidity and stability of sine-cones