{
  "abstract": "We establish a logarithmic Sobolev inequality for complete $C^{1,1}$ immersed submanifolds of dimension $m\\ge2$ in Cartan--Hadamard manifolds with sectional curvature at most $-b^2$. The inequality retains the Euclidean sharp constant after subtraction of $(m-1)^2b^2$ from the Fisher and mean-curvature energy; this coefficient is maximal for a lower bound uniform over $b\\ge0$. For immersed surfaces, we prove both a finite-domain critical exponential inequality and a global Ruf-type inequality with a positive $L^2$ term. Both have potential $|H|^2-b^2$, exponent $16π$ and an absolute multiplicative constant, and follow from one geometric heat-kernel comparison. The exponent and curvature coefficient are optimal. We classify Gaussian equality in the logarithmic inequality and geometric equality in the higher-dimensional Nash consequence. All inequality constants are independent of the codimension.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01610",
  "author_total": 2,
  "authors": [
    {
      "name": "Hongyu Chen"
    },
    {
      "name": "Li Ma"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9x9cag20ww7ev.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01610",
  "fulltext_url": null,
  "id": "9x9cag20ww7ev",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01610",
  "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"
    ],
    [
      "arxiv",
      "math.DG"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01610",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9x9cag20ww7ev.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.01610",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01610"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Logarithmic Sobolev and exponential inequalities for submanifolds in Cartan--Hadamard manifolds",
  "title_text": "Logarithmic Sobolev and exponential inequalities for submanifolds in Cartan--Hadamard manifolds",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/9x9cag20ww7ev",
  "venue": "arXiv",
  "versions": []
}