Spectral stability of the Kohn Laplacian under perturbations of the boundary

Abstract

In this paper, we study stability of the spectrum of the Kohn Laplacian □b on the boundary of a smoothly bounded domain in Cn as the boundary is perturbed in the C2-topology. We obtain estimates for spectral stability of the Kohn Laplacian on smooth compact hypersurfaces that satisfy uniform subelliptic estimate, in particular for strictly pseudoconvex hypersurfaces in Cn and pseudoconvex hypersurfaces of finite type in C2.