2025/04/17 by Yuri A. Kordyukov, Kordyukov, Yuri A.
Mathematics · #Advanced Harmonic Analysis Research #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Physics (math-ph) #Spectral Theory (math.SP)
paper · pdf · doi:10.48550/arxiv.2504.12928
openalex publication_date 2025/04/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
The Bochner-Schrödinger operator Hp=\frac 1pΔLp+V on high tensor powers Lp of a Hermitian line bundle L on a Riemannian manifold X of bounded geometry is studied under the assumption of non-degeneracy of the curvature form of L. For large p, the spectrum of Hp asymptotically coincides with the union of all local Landau levels of the operator at the points of X. Moreover, if the union of the local Landau levels over the complement of a compact subset of X has a gap, then the spectrum of Hp in the gap is discrete. The main result of the paper is the trace asymptotics formula associated with these eigenvalues. As a consequence, we get a Weyl type asymptotic formula for the eigenvalue counting function.