English

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.

Keywords

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

R2 v1 2026-07-01T08:14:23.072Z