{
  "abstract": "Let Δ = −div ∇. For a closed connected embedded minimal hypersurface Mⁿ ⊂ Sⁿ⁺¹, n ≥ 2, which is not totally geodesic, we prove the quadratic-form inequality Δ + |h|² ≥ n. Taking the test function equal to one gives Perdomo's average-curvature inequality, with equality precisely for minimal Clifford hypersurfaces. Let Q be a positive-definite self-adjoint endomorphism of ℝⁿ⁺¹ and let F(X) = ½⟨QX, X⟩. For a connected complete properly embedded hypersurface without boundary satisfying H = ⟨QX, ν⟩, where H = tr h, and which is not a hyperplane, we prove Δ_F + |h|² + ⟨Qν, ν⟩ ≥ 2λ_min(Q). Properness implies finite weighted volume. Equality in the corresponding average inequality characterizes generalized cylinders whose spherical factor lies in the least eigenspace of Q. In dimensions n ≥ 2, the isotropic case gives the sharp Gaussian average inequalities conjectured by Li and Zhao. The proofs construct a positive supersolution from the sum of two tangent-ball curvature functions. The singular parts of their distributional Hessians are retained in the weak inequality. Consequences include compact spectral comparisons, the embedded low-index classification, and a Bernstein theorem in specified eigendirections.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Anass Nifa"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0q6t60prtad1c.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.22999024",
  "fulltext_url": null,
  "id": "0q6t60prtad1c",
  "issns": [],
  "landing_url": "https://hal.science/hal-05769842v1",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "1.math.math-dg"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.science/hal-05769842/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0q6t60prtad1c.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:43Z",
      "native_id": "hal-05769842",
      "source": "hal",
      "url": "https://hal.science/hal-05769842v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-dg",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Sharp Schrödinger inequalities for embedded hypersurfaces",
  "title_text": "Sharp Schrödinger inequalities for embedded hypersurfaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:43Z",
  "url": "https://research.draconitic.com/paper/0q6t60prtad1c",
  "venue": "HAL",
  "versions": []
}