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arXiv 1908.032562019-08-08math.CVmath.AP

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

Siqi Fu, Weixia Zhu

备注：: 28 pages

英文摘要：

We study spectral stability of the $\bar\partial$-Neumann Laplacian on a bounded domain in $\mathbb{C}^n$ 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 $\mathbb{C}^n$, 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 $\mathbb{C}^n$.

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