The algebraic soliton linear stability conjecture

An algebraic soliton is a Ricci soliton arising algebraically, including the solvsolitons and nilsolitons considered in the paper. The algebraic soliton linear stability conjecture. Every algebraic soliton is strictly linearly stable, meaning that its linearized operator satisfies an estimate of the form

$$(\mathbf{L}h,h) \leq -\epsilon \|h\|^2$$

for some $\epsilon>0$ and all symmetric $2$-tensors $h$ in an appropriate tensor space.

The conjecture is motivated by a collection of stable algebraic solitons and the absence of known unstable examples. The supplied text does not state a resolution; the paper establishes stability for several families but leaves the general assertion open.