Eigenvalue comparison theorems for the Witten-Laplacian and the weighted $p$-Laplacian on complete manifolds with a modified Ricci curvature bounded from below

Abstract

In this paper, for complete manifolds with a modified Ricci curvature bounded from below, we can successfully set up Cheng-type eigenvalue comparison theorems for the first Dirichlet eigenvalues of the Witten-Laplacian and the weighted $p$-Laplacian on geodesic balls of these manifolds.

In March 2026, the main conclusions of this paper have already been announced roughly in Remark 1.22 of our previous work arXiv:2603.00942v2. However, until now, we find enough time to write down all the details. 18 pages. Comments are welcome