{
  "abstract": "In this paper, we study the ground states of attractive Bose-Einstein condensates in a bounded domain $Ω\\subset \\mathbb R^2$ under the ring-shaped trapping potential $$ V(x)=(|x|-1)^2. $$ The boundary geometry of $Ω$ may allow the ring $Γ=\\{x\\in\\mathbb R^2:|x|=1\\}$ of global minima for $V(x)$ to meet both the interior and the boundary of $Ω$. As the interaction strength approaches the critical value, we prove that if $Γ\\cap Ω\\not=\\emptyset$, the mass of ground states concentrates at a point $x_0\\inΓ\\cap Ω$ that has maximal distance from $\\partialΩ$. Our method relies on exponential upper and lower bounds for the difference between the bounded domain and whole space minimal energies. The essential lower bound follows from a uniform quadratic-growth estimate near the ground state manifold of the whole space problem, which is established by combining the nondegeneracy of the optimizer for the Gagliardo-Nirenberg inequality with a Lyapunov-Schmidt reduction.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.21994",
  "author_total": 3,
  "authors": [
    {
      "name": "Shubin Yu"
    },
    {
      "name": "Chun-Lei Tang"
    },
    {
      "name": "Ziheng Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ercvgwkhcx3pd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.21994",
  "fulltext_url": null,
  "id": "ercvgwkhcx3pd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.21994",
  "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",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7222645552",
  "pdf_url": "https://arxiv.org/pdf/2610.21994",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ercvgwkhcx3pd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.21994",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.21994"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Boundary geometry and concentration points for attractive Bose-Einstein condensates with a ring-shaped potential",
  "title_text": "Boundary geometry and concentration points for attractive Bose-Einstein condensates with a ring-shaped potential",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/ercvgwkhcx3pd",
  "venue": "arXiv",
  "versions": []
}