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arXiv · 2512.07263

The first nonzero eigenvalue of the weighted p-Laplacian on differential forms

Mingzhu Miao·Xuerong Qi·Jiabin Yin
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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.

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Mingzhu Miao, Xuerong Qi, Jiabin Yin. 2025-12-08. The first nonzero eigenvalue of the weighted p-Laplacian on differential forms. https://arxiv.org/abs/2512.07263

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