Spectral Stability of the $${\overline{\partial }}-$$Neumann Laplacian: Domain Perturbations
Siqi Fu, Weixia Zhu · Journal of Geometric Analysis · 2022
Abstract We study spectral stability of the $${\bar{\partial }}$$ ∂¯ -Neumann Laplacian on a bounded domain in $${\mathbb {C}}^n$$ Cn when the underlying domain is perturbed. In particular, we establish upper semi-continuity properties for the variational eigenvalues of the $${\bar{\partial }}$$ ∂¯ -Neumann Laplacian on bounded pseudoconvex domains in $${\mathbb {C}}^n$$ Cn , lower semi-continuity properties on pseudoconvex domains that satisfy property (P), and quantitative estimates on smooth bounded pseudoconvex domains of finite D’Angelo type in $${\mathbb {C}}^n$$ Cn .