The sub-exponential volume growth conjecture for the essential spectrum

Let $M$ be a complete non-compact Riemannian manifold whose Ricci curvature has a lower bound. Assume that the volume of $M$ grows uniformly sub-exponentially.

Sub-exponential volume growth conjecture. The $L^p$ essential spectrum of $M$ is $[0,+\infty)$ for any $p\in[1,+\infty]$.

This conjecture proposes that uniformly sub-exponential volume growth, together with a lower Ricci-curvature bound, determines the full nonnegative $L^p$ essential spectrum. The source provides no evidence of resolution, so its status remains open.