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A Convexity Result in the Spectral Geometry of Conformally Equivalent Metrics on Surfaces. (arXiv:1607.00396v3 [math.DG] UPDATED)
来源于:arXiv
Motivated by considerations of euclidean quantum gravity, we investigate a
central question of spectral geometry, namely the question of
reconstructability of compact Riemannian manifolds from the spectra of their
Laplace operators. To this end, we study analytic paths of metrics that induce
isospectral Laplace-Beltrami operators over oriented compact surfaces without
boundary. Applying perturbation theory, we show that sets of conformally
equivalent metrics on such surfaces contain no nontrivial convex subsets. This
indicates that cases where the manifolds cannot be reconstructed from their
spectra are highly constrained. 查看全文>>