On Isospectral compactness in conformal class for 4-manifolds

Xianfu Liu; Zuoqin Wang

On Isospectral compactness in conformal class for 4-manifolds

Spectral Theory 2017-05-29 v2 Differential Geometry

Authors: Xianfu Liu , Zuoqin Wang

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.

Keywords

riemannian geometry yamabe problem conformal geometry

Cite

@article{arxiv.1606.02070,
  title  = {On Isospectral compactness in conformal class for 4-manifolds},
  author = {Xianfu Liu and Zuoqin Wang},
  journal= {arXiv preprint arXiv:1606.02070},
  year   = {2017}
}

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