Spectral Stability of the $${\overline{\partial }}-$$Neumann Laplacian: Domain Perturbations

Autor: Siqi Fu, Weixia Zhu
Rok vydání: 2022
Předmět:
Zdroj: The Journal of Geometric Analysis. 32
ISSN: 1559-002X
1050-6926
DOI: 10.1007/s12220-021-00769-z
Popis: We study spectral stability of the $${\bar{\partial }}$$ ∂ ¯ -Neumann Laplacian on a bounded domain in $${\mathbb {C}}^n$$ 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 $${\mathbb {C}}^n$$ 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 $${\mathbb {C}}^n$$ C n .
Databáze: OpenAIRE
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