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

Author(s)
Siqi Fu, Weixia Zhu
Abstract

We study spectral stability of the ∂¯ -Neumann Laplacian on a bounded domain in C n 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 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 C n.

Organisation(s)
Department of Mathematics
External organisation(s)
Rutgers University
Journal
Journal of Geometric Analysis
Volume
32
No. of pages
34
ISSN
1050-6926
DOI
https://doi.org/10.1007/s12220-021-00769-z
Publication date
02-2022
Peer reviewed
Yes
Austrian Fields of Science 2012
101008 Complex analysis
Keywords
ASJC Scopus subject areas
Geometry and Topology
Portal url
https://ucris.univie.ac.at/portal/en/publications/spectral-stability-of-the-overlinepartialneumann-laplacian-domain-perturbations(df908519-3c2a-486d-953c-e9c9c3f1b738).html