On Isospectral compactness in conformal class for 4-manifolds

Xianfu Liu; Zuoqin Wang

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arXiv · 1606.02070

On Isospectral compactness in conformal class for 4-manifolds

Xianfu Liu·Zuoqin Wang

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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.

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Xianfu Liu, Zuoqin Wang. 2016-06-07. On Isospectral compactness in conformal class for 4-manifolds. https://arxiv.org/abs/1606.02070

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