Two results on nodal sets of eigenfunctions of sub-Laplacians

Cyril Letrouit (1)

1 DMA - Département de Mathématiques et Applications - ENS Paris

We prove two results concerning the nodal sets of eigenfunctions of sub-Laplacians. The first one asserts the validity in this setting of Courant's theorem on the number of nodal domains of eigenfunctions. The second one is the C/\sqrt{\lambda} density (with respect to the sub-Riemannian distance) of the nodal sets of eigenfunctions with eigenvalue \lambda.

Domaines: Mathématiques [math]; Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]; Théorie spectrale [math.SP]

Cyril Letrouit. Two results on nodal sets of eigenfunctions of sub-Laplacians. 2022. ⟨hal-03619388v1⟩