Klaus Kröncke: The spectrum of the Einstein operator on cones

The Einstein operator is an elliptic operator on symmetric 2-tensors which arises from linearizing the (Riemannian) Einstein equation. Linear stability of a given Einstein manifold is defined as the nonnegativity of the spectrum of the Einstein operator.

In general, the spectrum is very hard to compute. In this talk, we will show how commuting properties of the Einstein operator can be used to compute its spectrum on Ricci flat cones and sine-cones in terms of the spectrum on the link of the cones. Potential applications will also be discussed. This is partly based on joint work with Áron Szabó.