{
  "abstract": "We establish stability principles under compact gluing for the reverse square-root inequality and the Riesz transform. Below a common Sobolev dimension, the reverse estimate passes from finitely many model manifolds to their connected sum. A boundary-compatible Poisson parametrix also proves the Neumann reverse inequality for every $1<p<\\infty$ for real symmetric uniformly elliptic divergence-form operators on exterior Lipschitz domains. For the forward transform, we glue a bounded-core model and an independent whole-space end model that agree with the coefficients on overlapping regions. A homogeneous Fredholm construction then resolves the form-valued error. The resulting range is controlled by the two model exponents, with the additional restriction $p<n$ for Dirichlet data. More broadly, our method illuminates the interplay between the bounded interior and exterior problems, and provides a flexible framework for studying other boundary value problems.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.21399",
  "author_total": 1,
  "authors": [
    {
      "name": "Dangyang He"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6hmy3p61h0qgv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.21399",
  "fulltext_url": null,
  "id": "6hmy3p61h0qgv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.21399",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7213865196",
  "pdf_url": "https://arxiv.org/pdf/2609.21399",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6hmy3p61h0qgv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:07Z",
      "native_id": "2609.21399",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.21399"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Stability of the Riesz-type inequalities under gluing",
  "title_text": "Stability of the Riesz-type inequalities under gluing",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:07Z",
  "url": "https://research.draconitic.com/paper/6hmy3p61h0qgv",
  "venue": "arXiv",
  "versions": []
}