COMPACTNESS OF ISOSPECTRAL COMPACT MANIFOLDS WITH BOUNDED CURVATURES

Suppose that T-n(C) is the class of all Riemannian metrics on a given n-dimensional closed manifold such that their associated Laplacians (o n functions) have the same spectrum by counting multiplicities and the ir sectional curvatures are uniformly bounded /K/ less than or equal t o C by a constant C > 0. We show that the isospectral class T-n(C) is compact in the C-infinity-topology. This generalizes our previous C-in finity-compactness result, which holds for dimensions up to seven.