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arXiv · 2504.12666

Sublinear lower bounds of eigenvalues for twisted Laplacian on compact hyperbolic surfaces

Yulin Gong·Long Jin
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Abstract

We investigate the asymptotic spectral distribution of the twisted Laplacian associated with a real harmonic 1-form on a compact hyperbolic surface. In particular, we establish a sublinear lower bound on the number of eigenvalues in a sufficiently large strip determined by the pressure of the harmonic 1-form. Furthermore, following an observation by Anantharaman \cite{nalinideviation}, we show that quantum unique ergodicity fails to hold for certain twisted Laplacians.

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Yulin Gong, Long Jin. 2025-04-17. Sublinear lower bounds of eigenvalues for twisted Laplacian on compact hyperbolic surfaces. https://arxiv.org/abs/2504.12666

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