Consecutive eigenvalue gap conjecture for elliptic divergence-form operators

Let $M^n$ be a complete Riemannian manifold, let $\Omega\subset M^n$ be a bounded domain, and let $\lambda_k$ denote the Dirichlet eigenvalues of the operator $\mathcal{L}$ from Problem~, determined by the tensor $T$ and drifting function $\eta$. Consecutive eigenvalue gap conjecture. The upper bound for the gap between consecutive eigenvalues should be

$$\lambda_{k+1}-\lambda_k\leq C_{n,\Omega}k^{\frac{\delta}{n\varepsilon}},\qquad k>1,$$

where $C_{n,\Omega}$ is a constant dependent on $\Omega$, the dimension $n$ of $M$, the tensor $T$, and the drifting function $\eta$. This extends the conjecture of Chen, Zheng and Yang for the Laplace–Beltrami operator to the elliptic divergence-form operator considered here.