Spectra, rigidity and stability of sine-cones

Abstract

We compute the spectra of the Laplace-Beltrami operator, the connection Laplacian on 1-forms and the Einstein operator on symmetric 2-tensors on the sine-cone over a positive Einstein manifold $(M,g)$. We conclude under which conditions on $(M,g)$, the sine-cone is dynamically stable under the singular Ricci-de Turck flow and rigid as a singular Einstein manifold

35 pages, final version, to appear in J. Funct. Anal