Extremal Eigenvalues of the Laplacian in a Conformal Class of Metrics: The `Conformal Spectrum'

摘要

Let M be a compact connected manifold of dimension n endowed witha conformal class C ofRiemannian metrics of volume one. For any integer k ≥ 0, we consider the conformal invariant λ k c (C) defined as the supremum of the k-th eigenvalue λ k (g) of the Laplace–Beltrami operator Δ g , where g runs over C.