On the spectrum of non degenerate magnetic Laplacian - Sorbonne Université Access content directly
Journal Articles Analysis & PDE Year : 2021

On the spectrum of non degenerate magnetic Laplacian


We consider a compact Riemannian manifold with a Hermitian line bundle whose curvature is non degenerate. Under a general condition, the Laplacian acting on high tensor powers of the bundle exhibits gaps and clusters of eigenvalues. We prove that for each cluster, the number of eigenvalues that it contains, is given by a Riemann-Roch number. We also give a pointwise description of the Schwartz kernel of the spectral projectors onto the eigenstates of each cluster, similar to the Bergman kernel asymptotics of positive line bundles. Another result is that gaps and clusters also appear in local Weyl laws.
Fichier principal
Vignette du fichier
2109.05508v1.pdf (510.35 Ko) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

hal-04006297 , version 1 (23-05-2024)



Laurent Charles. On the spectrum of non degenerate magnetic Laplacian. Analysis & PDE, In press. ⟨hal-04006297⟩
13 View
0 Download



Gmail Mastodon Facebook X LinkedIn More