The first nonzero eigenvalue of the weighted p-Laplacian on differential forms
Differential Geometry
2025-12-09 v1
Abstract
We introduce the weighted p-Laplace operator acting on differential forms on a metric measure space, which is a natural generalization of the p-Laplace operator defined by Seto [32]. We obtain some sharp lower bounds of the first nonzero eigenvalue for the weighted p-Laplacian. Our results extend an estimate of Seto [32], as well as the eigenvalue estimates derived by Cui-Sun [8] for closed submanifolds.
Cite
@article{arxiv.2512.07263,
title = {The first nonzero eigenvalue of the weighted p-Laplacian on differential forms},
author = {Mingzhu Miao and Xuerong Qi and Jiabin Yin},
journal= {arXiv preprint arXiv:2512.07263},
year = {2025}
}
Comments
14 pages