{
  "abstract": "Let $Ω\\subset\\mathbb{R}^N$ be a bounded convex domain, and let $A=-Δ_D$ be the Dirichlet Laplacian. For every $s>0$ with $N>2s$, we prove that the Green-kernel transform $(x,y)\\mapsto K_{s,Ω}(x,y)^{-1/(N-2s)}$ extends continuously by zero to the diagonal and is jointly convex on $Ω\\timesΩ$. We prove that the regular part extends real analytically across the diagonal and that the associated Robin function is strictly convex and diverges to $+\\infty$ at the boundary. Hence it has a unique critical point. If $Ω$ is of class $C^{2,\\vartheta}$, this point is nondegenerate for every $s>0$ with $N>2s$. Moreover, the Hessian of the Robin function is positive definite throughout $Ω$ when $0<s<1$ or $N>3s$. The arguments combine convexity inequalities for Dirichlet heat kernels, a weighted boundary identity at fractional orders, and a finite-part transfer of Hessian positivity between spectral powers. In particular, the results apply to spectral fractional Dirichlet Laplacians and Navier polyharmonic operators.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.29288",
  "author_total": 2,
  "authors": [
    {
      "name": "Xiuda Liang"
    },
    {
      "name": "Wenjie Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5x1t015pt27jf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.29288",
  "fulltext_url": null,
  "id": "5x1t015pt27jf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.29288",
  "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.AP"
    ],
    [
      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W7214285205",
  "pdf_url": "https://arxiv.org/pdf/2609.29288",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5x1t015pt27jf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2609.29288",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.29288"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Convexity of inverse spectral Green kernels and nondegeneracy of Robin centers in convex domains",
  "title_text": "Convexity of inverse spectral Green kernels and nondegeneracy of Robin centers in convex domains",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/5x1t015pt27jf",
  "venue": "arXiv",
  "versions": []
}