Abstract:

We study spectral stability of the -Neumann Laplacian on a bounded domain in when the underlying domain is perturbed. In particular, we establish upper semi-continuity properties for the variational eigenvalues of the -Neumann Laplacian on bounded pseudoconvex domains in , lower semi-continuity properties on pseudoconvex domains that satisfy property , and quantitative estimates on smooth bounded pseudoconvex domains of finite D’Angelo type in . This talk is based on joint work with Siqi Fu.