Weyl law for singular Laplace-Beltrami operators


In this talk we present recent results on the asymptotic growth of eigenvalues of the Laplace-Beltrami operator on singular Riemannian manifolds, where all geometrical invariants appearing in classical spectral asymptotics are unbounded, and the total volume can be infinite. Under suitable assumptions on the curvature blow-up, we show how the presence of the singularity influences the Weyl’s asymptotics. Finally, we present a procedure to construct metrics with prescribed Weyl law, with a non-classical leading term.

Leiden, Netherlands