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On compactness of isospectral conformal, metrics of 4-manifolds

Published online by Cambridge University Press:  22 January 2016

Xingwang Xu
Xingwang Xu*
Affiliation:
Department of Mathematics, National University of Singapore, Singapore 0511, E-mail address: [email protected]
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In this paper, we are interested in the compactness of isospectral conformal metrics in dimension 4.

Let us recall the definition of the isospectral metrics. Two Riemannian metrics g, g′ on a compact manifold are said to be isospectral if their associated Laplace operators on functions have identical spectrum. There are now numeruos examples of compact Riemannian manifolds which admit more than two metrics such that they are isospectral but not isometric. That is to say that the eigenvalues of the Laplace operator Δ on the functions do not necessarily determine the isometry class of (M, g). If we further require the metrics stay in the same conformal class, the spectrum of Laplace operator still does not determine the metric uniquely ([BG], [BPY]).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 140 , December 1995 , pp. 77 - 99
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1995

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