{
  "abstract": "Let $Ω\\subset\\mathbb{C}^{n}$ be a bounded domain, and let $ρ:Ω\\to[-1,0)$ be a smooth strictly plurisubharmonic exhaustion function. We consider the logarithmic potential $g=-\\log(-ρ)$ and the associated complete Kähler metric $ω=dd^{c} g$. We prove that if $ρ$ satisfies the finite weighted Monge-Ampère mass condition with weight $(-ρ)^{\\varepsilon}$ for every $\\varepsilon>0$, then the spectrum and the essential spectrum of the Laplace-Beltrami operator of $(Ω,ω)$ both coincide with $[n^{2},\\infty)$. In particular, the bottom of the spectrum satisfies $λ_{0}(Δ_ω,Ω)=n^{2}$, and $n^{2}$ is not an $L^{2}$-eigenvalue. For each $α> \\frac{n}{2}$, we set $f=(-ρ)^α$ and prove that $f$ belongs to $W^{1,2}(Ω,ω)$ if and only if the Monge-Ampère mass of $ρ$ weighted by $(-ρ)^{2α-n}$ is finite. The integral identities underlying this equivalence, applied to the complex powers $(-ρ)^{α+it}$, give, after normalization, a singular Weyl sequence at every $n^{2}+4t^{2}$, $t\\in\\mathbb{R}$, as $α\\downarrow\\frac{n}{2}$. Combining our theorem with Cegrell's finite-mass exhaustion theorem, we obtain a complete Kähler metric with spectrum and essential spectrum equal to $[n^{2},\\infty)$ on every bounded hyperconvex domain.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.03036",
  "author_total": 2,
  "authors": [
    {
      "name": "Young-Jun Choi"
    },
    {
      "name": "Jiwon Brandon Jeong"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9me51tw8aj33r.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.03036",
  "fulltext_url": null,
  "id": "9me51tw8aj33r",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.03036",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CV"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2608|Geometry and complex manifolds"
    ]
  ],
  "openalex": "W7167628257",
  "pdf_url": "https://arxiv.org/pdf/2607.03036",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9me51tw8aj33r.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2607.03036",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.03036"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Spectrum of Complete Kähler Metrics on Bounded Hyperconvex Domains",
  "title_text": "Spectrum of Complete Kähler Metrics on Bounded Hyperconvex Domains",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/9me51tw8aj33r",
  "venue": "arXiv",
  "versions": []
}