Weighted heat kernel comparison theorems and its applications in spectral geometry
arXiv:2603.00942
Abstract
In this paper, we firstly establish weighted heat kernel comparison theorems for the weighted heat equation on complete manifolds with radial curvatures bounded, and then by mainly using this conclusion, we can obtain two eigenvalue comparison theorems for the first Dirichlet eigenvalue of the Witten-Laplacian as applications in spectral geometry.
49 pages. Several revisions have been made to v1, and an Appendix C has been added. Comments are welcome