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We study spectral stability of the $\bar\partial$-Neumann Laplacian on abounded domain in $\mathbb{C}^n$ when the underlying domain is perturbed. Inparticular, we establish upper semi-continuity properties for the variationaleigenvalues of the $\bar\partial$-Neumann Laplacian on bounded pseudoconvexdomains in $\mathbb{C}^n$, lower semi-continuity properties on pseudoconvexdomains that satisfy property ($P$), and quantitative estimates on smoothbounded pseudoconvex domains of finite D'Angelo type in $\mathbb{C}^n$.

Spectral Stability of the $\bar\partial-$Neumann Laplacian: Domain Perturbations