Weighted eigenvalues of Dirac operators: complete continuity and comparison
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 Lp 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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