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.