Weighted eigenvalues of Dirac operators: complete continuity and comparison

Zixuan Qiu; Ruijun Wu

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arXiv · 2508.07591

Weighted eigenvalues of Dirac operators: complete continuity and comparison

Zixuan Qiu·Ruijun Wu

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Abstract

We give a min-max characterization of the weighted Dirac eigenvalues, and show that the weighted eigenvalues and eigenspaces of Dirac operators are continuous with respect to weak $L^p$ convergence of the inverse weight, for any $p>n$. Moreover, we establish a comparison result for such weighted eigenvalue problems when there are no harmonic spinors.

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Zixuan Qiu, Ruijun Wu. 2025-08-27. Weighted eigenvalues of Dirac operators: complete continuity and comparison. https://arxiv.org/abs/2508.07591

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