@article{4c84b9f249ce4e86bb512aa02fc034d8,
title = "Spectral Stability of the ∂¯ - Neumann Laplacian: Domain Perturbations",
abstract = "We study spectral stability of the ∂¯ -Neumann Laplacian on a bounded domain in Cn 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 Cn, lower semi-continuity properties on pseudoconvex domains that satisfy property (P), and quantitative estimates on smooth bounded pseudoconvex domains of finite D{\textquoteright}Angelo type in Cn.",
keywords = "Finite type condition, Property (P), Pseudoconvex domain, Spectrum, Stability, The ∂¯ -Neumann Laplacian",
author = "Siqi Fu and Weixia Zhu",
note = "Funding Information: Part of this work was done during the visits of the first author to Princeton University, the University of Notre Dame, and Xiamen University, and the second to Rutgers University-Camden, and both to the Erwin Schr{\"o}dinger Institute. The authors thank these institutions for hospitality. The second author also thanks Professor Chunhui Qiu for his kind encouragement and support. The first author was supported in part by a grant from the National Science Foundation. The second author was supported in part by a grant from the National Natural Science Foundation of China (Grant No. 11971401). Funding Information: Part of this work was done during the visits of the first author to Princeton University, the University of Notre Dame, and Xiamen University, and the second to Rutgers University-Camden, and both to the Erwin Schr?dinger Institute. The authors thank these institutions for hospitality. The second author also thanks Professor Chunhui Qiu for his kind encouragement and support. The first author was supported in part by a grant from the National Science Foundation. The second author was supported in part by a grant from the National Natural Science Foundation of China (Grant No.?11971401). Publisher Copyright: {\textcopyright} 2021, The Author(s).",
year = "2022",
month = feb,
doi = "10.1007/s12220-021-00769-z",
language = "English (US)",
volume = "32",
journal = "Journal of Geometric Analysis",
issn = "1050-6926",
publisher = "Springer New York",
number = "2",
}