On Isospectral compactness in conformal class for 4-manifolds

Abstract

Let $(M,g_0)$ be a closed 4-manifold with positive Yamabe invariant and with $L^2$-small Weyl curvature tensor. Let $g_1\in [g_0]$ be any metric in the conformal class of $g_0$ whose scalar curvature is $L^2$-close to a constant. We prove that the set of Riemannian metrics in the conformal class $[g_0]$ that are isospectral to $g_1$ is compact in the $C^{\infty }$ topology.

References in corpus (1)

• Survey of the inverse spectral problem