Spectral Stability of the ∂¯ - Neumann Laplacian: Domain Perturbations

Siqi Fu, Weixia Zhu

Research output: Contribution to journalArticlepeer-review

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’Angelo type in Cn.

Original languageEnglish (US)
Article number57
JournalJournal of Geometric Analysis
Volume32
Issue number2
DOIs
StatePublished - Feb 2022

All Science Journal Classification (ASJC) codes

  • Geometry and Topology

Keywords

  • Finite type condition
  • Property (P)
  • Pseudoconvex domain
  • Spectrum
  • Stability
  • The ∂¯ -Neumann Laplacian

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